Shuttle regularly launched spy sats and was designed to grab an enemy one in a single orbit mission. Also Soviets believed it would nuke Moscow by sudden plane change via its wings & build their own version as a result.

That sounds military enough for me.

The Space Shuttle never had a combat mission, in the sense that it was never used to drop bombs via polar orbit over the Soviet Union. But of course it had tens of military missions, the Shuttle launched many department of defense satellites.