The 39-year-old Scot, back in the running for a seventh successive Ryder Cup in September, scored an eagle and seven birdies to move from six off the pace into a one-stroke lead over Barry Lane (67) and the American Jay Townsend (69). He is on a 10-under-par total of 134.
Torrance, whose victory in the Kronenbourg Open in Italy four weeks ago was his first for almost two years, said: 'Winning gives you confidence. I know I can do it and that makes it easier when you get yourself into contention again.'
His second round began spectacularly with seven successive threes - two pars, four birdies and an eagle on the 522-yard fifth, where he smashed a three-wood to 15 feet.
Out in 30, Torrance added three more birdies coming home to edge in front of his playing partner, Lane, and Townsend.