Jenkins will go straight into the Argyle squad for Saturday's League Two fixture at Morecambe.
The 21-year-old has made 95 appearances for Watford, but just one has come this season as he has struggled to break into Gianfranco Zola's new-look side.
"He's only 21, but he's got 80 Championship games under his belt," Plymouth boss Carl Fletcher told the club's official website. "We've obviously got a couple of injuries at the moment, with Paul Wotton and Jamie Lowry still out, so it'll be good for us to bolster that area of the squad.
"We earmarked him through our scouting network and then we spoke to people we know. I know someone who used to work at Watford with him and Nance [Kevin Nancekivell] knew someone different who worked there as well. And obviously we spoke to Rene [Gilmartin], who was there with him last year. They were all glowing references.
"He's keen, and obviously, with all the changes that have gone on at Watford, I think his chances might be a bit limited so he just wants to come and play that's ideal for us."