According to the CDC the risk of HIV transimission during a sporting is extremely low (low enough that there are no documented cases).
There was one karate school that went to court to deny access to a person who was HIV positive. Interestingly, the court thought that the karate school qualified as a public accomodation under the Americans with Disabilities Act, which makes it illegal to deny access to people based on their HIV status. It seems likely that most Aikido dojo would also be subject to similar regulation under the ADA, I would think. The karate school ended up winning the right to refuse access, based mainly on the argument that they practiced an extremely rough style that involved bleeding on a regular basis. Most Aikido schools would have probably have problems making a similar argument (thankfully - I'm perfectly happy with not bleeding on a regular basis