Law enforcement sources tell TMZ the ex-"Deadliest Catch" star and a lady friend drove down to Phoenix from Washington state last week for what they called a "vacation." We're told the woman is married ... but that the 2 have hung out like this before.

Friday morning, the woman told cops she discovered Jake had split from their hotel ... taking her car in the process. We're told she reported the car stolen when she couldn't get a hold of him, but called the cops when she found him at a Circle K the next day.

Phoenix PD officers showed up and searched him, where they say they found Xanax pills and crystal meth ... which we're told he admitted were for personal use. He was booked for 1 count of felony theft and 2 counts of felony drug possession.

This is the latest legal run-in for Jake -- who was busted for DUI in 2010, and then, on the flip side, was robbed, beaten and tossed from a vehicle in November in Washington. At the time his brother, Josh, said Jake was seriously injured.