We study single field slow-roll inflation in the presence of F(R) gravity in the Palatini formulation. In contrast to metric F(R), when rewritten in terms of an auxiliary field and moved to the Einstein frame, Palatini F(R) does not develop a new dynamical degree of freedom. However, it is not possible to solve analytically the constraint equation of the auxiliary field for a general F(R). We propose a method that allows us to circumvent this issue and compute the inflationary observables. We apply this method to test scenarios of the form F(R) = R + αRⁿ and find that, as in the previously known n = 2 case, a large α suppresses the tensor-to-scalar ratio r. We also find that models with F(R) increasing faster than R² for large R suffer from numerous problems.