Objective. Magnetic resonance (MR) is an innovative technology for online image guidance in conventional radiotherapy and is also starting to be considered for proton therapy as well. For MR-guided therapy, particularly for online plan adaptations, fast dose calculation is essential. Monte Carlo (MC) simulations, however, which are considered the gold standard for proton dose calculations, are very time-consuming. To address the need for an efficient dose calculation approach for MRI-guided proton therapy, we have developed a fast GPU-based modification of an analytical dose calculation algorithm incorporating beam deflections caused by magnetic fields. Approach. Proton beams (70-229 MeV) in orthogonal magnetic fields (0.5/1.5 T) were simulated using TOPAS-MC and central beam trajectories were extracted to generate look-up tables (LUTs) of incremental rotation angles as a function of water-equivalent depth. Beam trajectories are then reconstructed using these LUTs for the modified ray casting dose calculation. The algorithm was validated against MC in water, different materials and for four example patient cases, whereby it has also been fully incorporated into a treatment plan optimisation regime. Main results. Excellent agreement between analytical and MC dose distributions could be observed with sub-millimetre range deviations and differences in lateral shifts <2 mm even for high densities (1000 HU). 2%/2 mm gamma pass rates were comparable to the 0 T scenario and above 94.5% apart for the lung case. Further, comparable treatment plan quality could be achieved regardless of magnetic field strength. Significance. A new method for accurate and fast proton dose calculation in magnetic fields has been developed and successfully implemented for treatment plan optimisation.