Folk was released one day after he reportedly underwent an emergency appendectomy. He signed with the team on Oct. 30.
Forbath becomes the Patriots' fourth kicker this season, succeeding Stephen Gostkowski, Mike Nugent and Folk.
''(We) worked Kai out earlier this fall, three or four weeks ago, whatever it was,'' coach Bill Belichick said Friday. ''So we'll see how it goes.''
Originally signed by the Dallas Cowboys as a free agent out of UCLA in 2011, Forbath spent his rookie season on injured reserve. He has since kicked for Washington, New Orleans, Minnesota and Jacksonville.
Gostkowski, the kicker since 2006, was placed on the injured reserve on Oct. 2. He converted 7-of-8 field-goal attempts and 11-of-15 conversions in four games.
Nugent signed on Oct. 3 and was released on Oct. 29 after missing three of eight field-goal attempts and one point-after in four games. Folk appeared in three games, connecting on 7-of-9 field-goal attempts and all three PATs.
The Patriots' instability at kicker is something new. Adam Vinatieri handled the kicking from 1996-2005. Aside from an eight-game stint in 2010 when he was injured and Shayne Graham was brought in, Gostkowski has performed the duties since he was drafted 13 years ago. He is the franchise's scoring leader with 1,775 points.
''It has (been a challenging situation), but the other teams in the league have gone through it, and we've gone through it at other positions,'' Belichick said. ''It's not what you want. It's not ideal. But we'll keep going.''
''They've been great,'' Belichick said. ''Joe's got a lot of leadership, obviously the more experienced, but Jake's mature beyond his years.''
Forbath did not speak to the media, but Bailey said the newcomer's first day on the job went well.
''Only been around him for like two or three or four hours today. Really nice guy. Had a really good first day so just go from there,'' he said.
Added Cardona: ''Ultimately, our job is just to come out and be prepared for whoever's back there. There's been some turnover this year, but ultimately we're trying to make it as consistent as possible up front.''
NOTES: The Patriots have ruled tight end Ryan Izzo (illness) out of Sunday night's game at Houston.
Seventeen players are listed as questionable, many with the flu bug that has hit the locker room this week.