The midfielder will join up with the Rovers squad and complete the paperwork on Thursday.
Dorman, 29, has been granted permission to play in the Pirates' FA Cup clash with Corby on Saturday.
Buckle told the club's official website: "We have picked up a few injuries in the midfield of late, which has been a worry, and Andy will bring us some much needed experience and stability.
"He is a box-to-box player and his record shows that he can score goals. He made 23 appearances for a Championship side last year, and he is the perfect age for us.
"He will add lots of value to our squad and the fact he is available for Saturday's FA Cup game is a massive plus for us."