Barring special circumstances, which are always possible, it would be released tomorrow, Friday August 25, at 4 p.m. - according to the guidelines and process established over the past few days by the Fulton County Sheriff's Office for other defendants.
The sheriff's office has noted in emails to news organizations: "Release of booking information to include mugshots will occur daily at approximately 4:00 p.m. (EST) via media advisory."
With Trump arriving at the jail well after 4 p.m. on Thursday night, that would push the expected release of his mugshot to Friday.
So far, the sheriff's office has generally been consistent about following that. Both Wednesday and Thursday, emails went out with multiple mugshots from the co-defendants who turned themselves in that day.