Siemian, 31, was released by the Cincinnati Bengals in the preseason and joins Zach Wilson and Tim Boyle in the Jets' quarterback room. The move comes two days after another poor performance by Wilson, who nevertheless received a vote of confidence from coach Robert Saleh.
Wilson will start Sunday night against the Kansas City Chiefs, Saleh said, but Siemian gives the Jets a quarterback with starting experience -- a potential option if Wilson continues to struggle.
Meanwhile, former San Francisco 49ers quarterback Colin Kaepernick wrote a letter to Jets general manager Joe Douglas that was dated Sept. 21 asking that the team consider signing him to the practice squad, according to rapper J Cole. The letter was shared on Cole's Instagram account Tuesday.
"I asked Colin @kaepernick7 if I could share this letter with the world," Cole wrote. "He was reluctant. My argument was that I believe the people and all organizations should know the truth about how hard he works and how much he still wants to play. And always has. In the end, he agreed to let me."
Kaepernick, 35, has worked out for NFL teams, including the Las Vegas Raiders last year, but last played in the NFL in 2016, the year he began protesting racial inequality during the national anthem.
The Jets (1-2) are reeling because Aaron Rodgers went down with an Achilles tear on the fourth play of the season. Wilson came off the bench to help the Jets to an overtime win over the Buffalo Bills, but the offense has generated only three touchdowns in nearly three full games with him at quarterback.
Siemian's career record is 13-17, with 42 touchdowns and 28 interceptions. The Broncos' full-time starter in 2016 and 2017, Siemian has been relegated to backup duty since being released by Denver.
He hasn't won a start since 2017. Since then, he has dropped six consecutive starts, including one for the Jets in 2019. In Week 2 of that season, he replaced Sam Darnold, who was out with mononucleosis, but lasted only one quarter after suffering a season-ending ankle injury on a hit by Cleveland Browns defensive end Myles Garrett.
Siemian started against the Jets last season while playing for the Chicago Bears. He struggled in a 31-10 loss, as he completed 14 of 25 passes for 179 yards with one touchdown and one interception.
This summer, he lost out to Jake Browning for the Bengals' backup job. Siemian got a lot of playing time in the preseason, but he completed 36 of 65 passes for 316 yards with no touchdowns and two interceptions.
Since Rodgers' injury, the Jets have been linked to available quarterbacks such as Carson Wentz, Matt Ryan and Chad Henne. They expressed interest in Henne, who played under offensive coordinator Nathaniel Hackett in Jacksonville, but Henne declined. The Jets reportedly rejected overtures from Wentz and Ryan.