The team announced Friday they have waived the cornerback.
The move comes after Jenkins called a fan on Twitter a slur earlier this week, then refused to apologize for it on Thursday.
"This was an organizational decision," coach Pat Shurmur said in a statement. "From ownership to management to our football operations, we felt it was in the best interests of the franchise and the player. Obviously, what happened this week, and the refusal to acknowledge the inappropriate and offensive language, was the determining factor."
The eight-year pro will go on waivers.
Jenkins responded to the news of getting cut by tweeting "Best news ever.. Thank you."
The 31-year-old corner has been a thorn in the organization's side for much of the season, including blaming the pass rush for the defense's poor play early in the season and later complaining about not traveling with top receivers.
For the season, Jenkins compiled four interceptions, 14 passes defended and 54 tackles in 13 games. He has been the Giants' best corner this season, but that isn't saying much. Pro Football Focus ranks Jenkins the 55th rated CB on the season.