Batch, 37, has started just three games in the last four seasons. In his only start last season, Batch threw for 208 yards in a 27-0 win over the St. Louis Rams.
Leftwich struggled against the Baltimore Ravens last week. He completed 46 percent of his passes for 201 yards and no touchdowns. He also threw an interception in the 13-10 loss.
Batch has been with the Pittsburgh Steelers since 2003. He's started seven of 32 games in that span, completing 57 percent of his passes for 1,594 yards and 11 touchdowns. He's thrown eight interceptions.
The Steelers enter Sunday's game with a 6-4 record. The Browns are 2-8 this season.