Cody Bellinger's hot streak continues -- and here's the proof. 

The 22-year-old Dodgers rookie phenom has been dating Melyssa Perez -- a pre-law student at the University of Texas (hook 'em), TMZ Sports has learned. 

Our sources say the two aren't official or anything ... but they've been on a few dates and he's brought her to the stadium -- even bringing her on the field and into the dugout.  

Our Dodgers spies tell us the two were even seen getting kissy and cuddly after the Dodgers beat the White Sox earlier this week. 

Kid's havin' a season, huh?!