Rodriguez, a fourth-round pick of the Chicago Bears last season, was released in June following his second legal incident in three months.
In March, Rodriguez was arrested in Miami Beach, Fla., and charged with resisting an officer without violence, as well as disorderly intoxication. Those charges were eventually dropped.
However, Rodriguez was arrested again on May 31, charged with driving under the influence after being stopped by Illinois State Police. Rodriguez received a ticket but was not suspended by the NFL.
The Bears cut ties with Rodriguez soon after. He spent training camp with the Miami Dolphins before being released during final cuts.
On Monday, Bills coach Doug Marrone was asked how the organization decides to sign a player with recent legal troubles, like Rodriguez.
"I just think it’s a lot of decisions go into it. Where that person is now in their life, have they learned from that mistake and then what it was and being evaluated," he said. "Are you going to better your roster? But I think the first thing I know, and not speaking for Doug (Whaley) or Russ (Brandon), is obviously character is a big thing, especially coming onto this team. I think sometimes, and it’s different, people will take their views differently."
The expectation is that the Bills will have little tolerance for any additional problems from Rodriguez, who has been out of football for two months and becomes the second fullback on the roster.
"When someone comes along, you know there is a short leash," Marrone said. "They have to convince people that they’ve learned from that mistake, that they’re ready to move on, and then once they do that they have to get on the field and obviously perform."
Marrone said Rodriguez, who is 6-foot-2 and 245 pounds, projects as an H-back (a combination of a fullback and tight end, often put in motion, who can be used as both a pass-catcher and blocker) and a special teams contributor. Like Marrone, Rodriguez is a Bronx, N.Y., native.