They do not have a delivery system, that would have to be a rocket launch similiar to NASA capabilites. Be assured that we know every particle that is sent into space and it would be shot down in minutes.
Unless they launched it off a cargo ship 50 miles off shore.
A nuclear explosion need not occur in orbit to be potentially damaging. Any country with the ability to launch an intermediate-range ballistic missile — Pakistan, for example — is capable of lofting a nuclear warhead to the altitude needed to cause damage to satellites. According to space policy analyst
Henry Spencer, “...[N]uclear explosions can badly damage satellites even at very long range... the X-ray pulse -- which carries much of the energy of a bomb exploded in vacuum... kicks up ionization in the outer surface of [a given] satellite, and the resulting electrical phenomena are quite destructive... A large nuclear explosion -- or a bunch of small ones -- anywhere within, say, the Earth-Moon system could wreak havoc with all satellites within line of sight.” In other words, a hypothetical terrorist group could launch a nuclear missile stright up into space and “zap” every satelllite above the horizon of its warhead at the time of its explosion. By carefully timing their launch, these terrorists could poke a big hole in, say, a GPS or MilStar constellation.