As Quora User said, the U.S. does contribute quite a lot to CERN projects. There's a lot of information on U.S. contributions to the LHC on this page: US/LHC - Large Hadron Collider Prior to the LHC, big collider projects were smaller and more regional. read more
United States does fund CERN projects as explained above. The question may be why does it not fund more. The answer is that the US has its own particle accelerator and conducts its own research at Argonne National Laboratory and Fermi lab in Illinois. read more
CERN is run by 22 member states, and many non-European countries are involved in different ways This content is archived on the CERN Document Server The CERN convention was signed in 1953 by the 12 founding states Belgium, Denmark, France, the Federal Republic of Germany, Greece, Italy, the Netherlands, Norway, Sweden, Switzerland, the United Kingdom and Yugoslavia, and entered into force on 29 September 1954. read more
CERN is composed of European member states, with the US not being European, it is not a member. Additionally, the US has its own national laboratories and universities. The Large Hadron Collider is without a doubt the best known modern day project at CERN so I will use that for my examples. read more