During the 20 months in which he has presided over in a 9,200 square miles in the western state of Arizona, Mr Arpaio has done just that. He proudly boasts that he has amassed an army of volunteers, some of whom patrolled streets on horses wearing police uniforms, Stetsons, and pistols.
The sheriff, a blunt man of Italian origin with a boyhood passion for Westerns, has chosen the right place in which to deploy his Wild West tactics. Most of Arizona's 3.8 million residents are conservative, and - like many Americans - deeply anxious about crime.
Mr Arpaio says that his posse appeals to the popular imagination, even though they pursue car thieves rather than rustlers. 'I have hit a nerve,' he explained, 'People here are angry.'
The unpaid force of 2,300 has not been idle. Before Christmas, after several car-jackings, pos semen on horseback paraded in shopping malls, escorting shoppers from store to store. Then the sheriff dispatched his troopers to clear prostitutes from a red-light district, instructing his posse - a mostly white, male collection of lawyers, blue-collar workers, executives, and retirees - to follow the women around until they left.
In June he announced that he was mobilising 600 armed posse members, supported by helicopters, armoured cars, and police- dog units, to eradicate crime in south-west Phoenix. Although 'Operation Summer Heat' led to 104 arrests, 40 drugs seizures and the recovery of 17 stolen cars, not everyone was impressed. Some residents complained that they were too zealous: within a month, they issued 1,500 traffic tickets.
Yet criticism of his gung-ho methods has been muted, largely because Arizona lacks a strong liberal voice. The sheriff's legal right to spirit up a posse of local worthies derives from America's frontier days, and - Mr Arpaio claims - can be traced back to English laws during Alfred the Great's time. Louis Rhodes, head of the Phoenix chapter of the American Civil Liberties Union, is one of the few to complain that its modern manifestation smacks strongly of vigilantism - and even fascism.
'Arpaio's posse are a bunch of junior G-men who want to be Batman. It's a comic-book version of crime-fighting and I'm worried that some bad will eventually happen. All the ingredients are there.' No statistics exist which prove that the posse has helped to reduce crime overall, he said.
Sheriff Arpaio is unconcerned. He says that his posse makes up for the 30 vacancies which he cannot afford to fill in his police force, is very cheap to run, and is properly trained. The 800 posse members permitted to carry guns have received the same weapons training as full-time officers - a minimum of 56 hours.
Posse members can only make arrests under the supervision of a full-time deputy, and can only draw a gun if their life is threatened. The sheriff dismisses as insignificant the fact that several of his would-be cops have been kicked out of the posse for being drunk or carrying concealed weapons - or that one posseman is 86.
The pleasure he takes in his scheme may be because his 'hang'em and flog'em' tactics have made him the best-loved politician in the state, more revered than the Republican governor, Fife Symington (also in his posse). 'I receive hundreds of letters a month, of which 99 per cent are favourable,' he said, leaning back happily in his chair, 'Everybody loves me. They want me to run for president.'
Much of this has to do with his publicity skills. On a visit to the sheriff's office the Independent was provided with a resume of the gun battles he fought with Turkish and Mexican drug smugglers during his career with the US Drug Enforcement Administration, an account of his numerous appearances on national television, and a plastic sheriff's badge bearing his name.
Yet he has also won a lot of support for the other, equally controversial, aspect of his anti-crime policy. Arguing that he lacks dollars 42m (dollars 28m) to build a new jail, Mr Arpaio has created a tented camp in Phoenix in which he houses 1,000 inmates. Any suggestion that this is inhumane solution to overcrowding gets short shrift: 'So it happens to be in the desert? So what? So it happens to be 118 degrees out there. So what? Our soldiers survived in tents during the Gulf war, didn't they? And they didn't commit any crimes.'
His recent revisions to the jail rules confirm that the sheriff, a staunch Republican, favours a punitive rather than remedial penal system. Although many of his 5,500 prisoners are unconvicted and awaiting trial, he has banned smoking, long hair, pornographic magazines, and videos with an over-17 rating.
'I told them they could only watch Lassie Come Home or Donald Duck. If they are in jail, why should they be watching violent videos at the public's expense?'
When Sheriff Arpaio visited the camp last week he was greeted with scattered boos and a few bellowed demands for cold water as he tramped around behind the 20ft razor-wire fences. The inmates - mostly low-risk prisoners on work programmes - included Anthony White, 20, who said he was serving 10 days because he could not afford to pay dollars 300 to take court-ordered therapy classes, to which he was sentenced following a drunken fracas.
'It is hotter than hell in here,' he said. The two evaporative coolers in his tent, which contained 20 men, made no impact on the intense desert heat. 'This is not a reasonable punishment for what I did. Dogs get treated better than this at dog farms.'
But most of the prisoners - some had been consigned to swelter in the desert for non-payment of traffic fines - appeared resigned to their lot.
As he strode between the tents, bantering with his wards as they sheltered from the fierce sun, the sheriff was the one with the loudest complaint.
'It's only 110 degrees today. Not hot enough] I like it much better when it's 130.'