Smith made Cleveland's roster last season as an undrafted free agent. He played in three games and spent 11 weeks on the team's practice squad.
Acho, who started 48 career games at Texas, was selected in the sixth round. His signing leaves running back Trent Richardson and quarterback Brandon Weeden - the club's two first-round picks - as the only unsigned rookies.
The 6-foot-1, 245-pound Dickson was signed by Jacksonville last July, but waived by the Jaguars before the regular season.
Thomas participated in the Browns' rookie minicamp last weekend on a tryout basis. He was a four-year letter winner at Toledo.