Mr Cecil faces two years in jail if convicted. The Ugandan parliament is considering legislation aimed at increasing penalties for homosexual acts.
The play, which tells the story of a gay businessman killed by his own employees, was performed at two theatres in the Ugandan capital, Kampala, last month. Uganda's Daily Monitor newspaper reports that the Media Council had warned the play's backers not to perform it until it had been approved.
Mr Cecil was freed on bail of 500,000 shillings ($200; £124). He was ordered to surrender his passport and must report back to court on 18 October.
His lawyer John Francis Onyango told the AFP news agency that his client was in good health.
Homosexual acts are illegal in Uganda and gay people have faced physical attacks and social rejection.
An anti-gay bill imposing life sentences on those convicted of homosexual acts was re-tabled in parliament earlier this year.
It was first introduced in 2009 but never debated - and the MP backing the legislation says a clause proposing the death penalty will be dropped