Majorana zero modes have been proposed as building blocks of intrinsically fault-tolerant quantum computers. Currently, externally applied magnetic fields are necessary to induce Majorana zero modes in carefully engineered systems. Topological qubit state readout is realized by parity sensing of Majorana islands. However, fast and high fidelity conventional cQED parity readout is incompatible with the magnetic fields needed for Majorana physics. In this thesis, magnetic field insensitive microwave CPW resonators with artificial Abrikosov vortex pinning sites have tested and implemented in a graphene based transmon qubit. It has been shown that these artificial pinning sites reliably trap vortices and are able to retain their zero field Qi ~ 105 up to perpendicular fields of 35 mT. By application of these resonators, we have described the successful continuous wave qubit spectroscopy of a graphene transmon qubit at B|| = 1 T with a minimal linewidth of 166 MHz and demonstrated manipulation of the qubit frequency between 3.2-7 GHz with electric field. This is the first ever measured superconducting qubit that shows these properties at a magnetic field of 1 T.