“Tortious” is defined by the American Heritage Dictionary as the adjective form of the noun “tort,” so “tortious conduct” is conduct that constitutes a tort. “Tortuous” is defined as:
1. Having or marked by repeated turns or bends; winding or twisting: a tortuous road through the mountains.
2. Not straightforward; circuitous; devious: a tortuous plot; tortuous reasoning.
3. Highly involved; complex: tortuous legal procedures.
And usage reflects this; the customary adjective form of “tort” in legal American English is indeed “tortious” — for instance, a Westlaw ALLCASES search for “tortious conduct” & date(> 1/1/2013) yields 1574 results, and for “tortuous conduct” & date(> 1/1/2013) yields 48. Google Ngrams reports even more preference for “tortious conduct.” When the split is so lopsided, this suggests that the rarer usage is likely to be perceived as an error, and in any event is likely to be distracting. So “tort” goes with “tortious.”