Named Twerton Park since 1932, chairman Manda Rigby is allowing supporters the opportunity if they each pay a £50 fee. The winner will be picked out of a hat.
"We pride ourselves on being innovative at Bath City, and the stadium name draw is just the most recent example," Rigby is quoted inThe Guardian as saying.
"We hope that businesses locally and nationally will recognise the tremendous value of acquiring the naming rights to our ground for just £50 but we also want our fans and the general public to get involved as well."
The Romans, who currently sit at the foot of the Blue Square Conference, are hoping the idea helps them financially.
Captain Jim Rollo, who has made over 450 appearances for the club, believes the draw is "a brilliant idea".
Top flight clubs such as Manchester City and Newcastle United have recently renamed their grounds in huge multi-million pound sponsorship deals.
Bath City's most famous fan is film director Ken Loach.
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