He celebrated by scoring for the Iron in their win over Wycombe on Saturday.
"I have signed until the end of the season," Parkin told the club's official website. "Beyond there it is a case of wait and see what happens with Cardiff.
"I haven't spoken to the gaffer here about anything after that. For now, I am delighted to be here."
Iron boss Alan Knill added: "He's a big presence for us and adds something different that we didn't already have.
"He's fitted well into the team and the club and has a big part to play for the remainder of the season."