Taylor is a former Washington Redskins safety who wore No. 21 and was killed in 2007 after he was shot when intruders entered his home. He was 24 years old.
The Giants called Taylor a role model of Collins, while Collins said Taylor is his idol and thanked New York cornerback Dominique Rodgers-Cromartie for allowing him to have the number.
Rodgers-Cromartie will now wear No. 41, the team said.
Collins was the Giants' second-round draft pick last month. He was an All-American at Alabama in 2014.
- Molly Geary