Burroughs was probably introduced to Aleister Crowley by Robert Anton Wilson. Wilson sent him a copy of Illuminatus! which features both Crowley and Burroughs (thus popularizing the '23 Enigma' joke). According to RAW, it was after that that Burroughs started mentioning Crowley. It's obvious that in some ways the two are kindred souls.
This is from an interview by Burroughs with Jimmy Page (whose connections with Crowley are well known):