The United States, Russia, and China all have some space weapon capability. The question going forward should be how these nations can come together and agree to limit (and possibly eliminate, ha ha) space weapons.
China and Russia have been pushing for a debate on a Prevention of an Arms Race in Outer Space (PAROS) treaty, which would ensure that states observe a prohibition on space weaponization. Russia and China have also submitted a draft treaty to the UN preventing the placement of weapons in outer space. However, in all likelihood, the United States would not want an arms-control treaty if it means limiting the U.S. National Missile Defense system (which has de facto ASAT applications).