After the 2012 NFL Draft concluded, Wedige signed with the Arizona Cardinals as an undrafted free agent, but was eventually let go during the final wave of roster cuts. That same season, he was signed with the New York Giants to join the practice squad, but was cut from it two weeks later.
That's when The Bengals signed him to their practice squad, but he was eventually signed to the Cardinals’ 53-man roster, and he would spend the next year with the team until he was cut in August of this past year.
After that, he was signed by the New York Jets, but was eventually cut before the Bengals signed him to their PS last season.
The bengals have already cut starting center Kyle Cook this offseason, and as long as they don't select one early in May's NFL Draft, he's the favorite to win the starting job in training camp.