Again, what type of welder do you have access to? For the record, any process that uses an electric arc to generate the heat for welding is an "Arc'" type welder.
Do you mean Shielded Metal Arc Welding (Stick)(AC or DC)? Gas Metal Arc Welding (Mig and/or Flux Core)? How about Gas Tungsten Arc Welding (Tig)? All are doable, and all can be used to build a kart; you just need to know what the limitations are for each process.
Gas Welding and Braze Welding traditionally use Oxygen/Acetylene for fuel to generate the heat needed for welding. They are both viable types to build a kart with, but require totally different equipment and techniques compared to any of the electrical Arc processes.