Using numerical simulations of lattice QCD we calculate the effect of an external magnetic field on the equation of state of the quark-gluon plasma. The results are obtained using a Taylor expansion of the pressure with respect to the magnetic field for the first time. The coefficients of the expansion are computed to second order in the magnetic field. Our setup for the external magnetic field avoids complications arising from toroidal boundary conditions, making a Taylor series expansion straightforward. This study is exploratory and is meant to serve as a proof of principle.