William Hicks claims Soulja was a no-show after he booked the rapper to perform back in April in Birmingham, AL. According to legal docs obtained by TMZ ... promoter Hicks says he paid Soulja a deposit of nearly $9k up front.

Hicks, however, claims moments before Soulja was supposed to perform, the rapper's manager texted him saying he wasn't gonna make it 'cause he missed his flight. According to docs ... Hicks wasn't buying the excuse, claiming Soulja was partying in Vegas and performing there instead.

As we first reported ... Hicks fired off a legal letter to Soulja's team back in April demanding repayment or face a lawsuit. Hicks never got his money so he called out Soulja on social media, prompting this response from the rapper:

According to the lawsuit ... Hicks says Soulja sent him a video apologizing for skipping out on the gig but Hicks wanted the rapper to publicly apologize. Hicks says Soulja refused, which is odd since an apology video can be found on YouTube.

For his part, sources close to Soulja say he was in negotiations with Hicks, and they were trying to work out an agreement. However, communication stopped when Soulja was arrested, and was sentenced to 240 days behind bars.

Nevertheless ... Hicks is suing for breach of contract and the money he's out ... to the tune of $13,487.85. As we reported, Soulja got out of jail on Sunday -- so ya win some, ya lose some.