Here's the transcript of the High Court decision that declined his appeal.

http://www.judiciary.gov.uk/Resources/JCO/Documents/Judgment...

"Rape - On 17 August 2010, in the home of the injured party [SW] in Enköping, Assange deliberately consummated sexual intercourse with her by improperly exploiting that she, due to sleep, was in a helpless state. It is an aggravating circumstance that Assange, who was aware that it was the expressed wish of the injured party and a prerequisite of sexual intercourse that a condom be used, still consummated unprotected sexual intercourse with her. The sexual act was designed to violate the injured party’s sexual integrity."

I would consider that to be rape, but I have no idea whether the US in general or legally would agree.