It has previously been shown that quantum state tomography can be used to increase the key rate of quantum key distribution (QKD) for the special case of qubits (i.e.,d=2). Here, we consider the case of higher dimensions, i.e., qudits, and show that, for a prime number d>2, quantum state tomography can also improve the key rate of d-dimensional qudit-based QKD schemes, compared to the standard (d+1)-basis protocol. We apply our results to previous QKD experiments based on OAM (orbital angular momentum) encoding and demonstrate the advantage of tomography-based QKD protocols. Moreover, we compare the key rate of tomography-based QKD protocol with reference-frame-independent QKD protocol. We show that, for a rotation channel, the two protocols give the same key rate. However, for any other channels, tomography-based QKD protocol always gives a higher key rate than reference-frame-independent QKD protocol.