Clayton has been without a club since leaving Birmingham last year and is keen to get his career going once more after a difficult past few years.
Clayton, likely to have to settle for a place on the bench in Saturday's League One home game with Plymouth Argyle, said: "I had a few offers higher than this, but they weren't right for my personal situation.
"So I was delighted to come in and are not fazed by where we are in this league. I know in this league that if you win a few games, we can bounce right back.
"There is no fear factor of where we are in this league.
"I feel we have just as good a chance to get out of this situation than go down. The worst case scenario is if we do go down, we will have one of the strongest squads next year to bounce straight back up. But I am not looking that, to be honest and just wanted to sink my teeth into a project which was going somewhere."
Meanwhile, Rovers chief Gary McSheffrey is hoping to do further business in a busy window after following up the signing of Clayton with the addition of former Huddersfield Town loan striker Mipo Odubeko.
Odubeko's arrival preceded the exit of Omar Bogle, who has left the club by mutual consent. He has linked up with Hartlepool United.
McSheffrey, speaking at his pre-match press conference on Thursday, commented: “We’re looking, we’re speaking to a couple of people and we’ll make decisions on which options we take up.
“There could still be something.
“We might still bring in one more in the defensive area and we might still bring in one more in the attacking area.
“We’ve still got one more loan to our disposal. We’re waiting on discussions that are taking place.
“If anything happens it’ll probably be in the next couple of days."