  We control transition frequency of a superconducting flux qubit coupled to a
frequency-tunable resonator comprising a direct current superconducting quantum
interference device (dc-SQUID) by microwave driving. The dc-SQUID mediates the
coupling between microwave photons in the resonator and a flux qubit. The
polarity of the frequency shift depends on the sign of the flux bias for the
qubit and can be both positive and negative. The absolute value of the
frequency shift becomes larger by increasing the photon number in the
resonator. These behaviors are reproduced by a model considering the magnetic
interaction between the flux qubit and dc-SQUID. The tuning range of the
transition frequency of the flux qubit reaches $\approx$ 1.9 GHz, which is much
larger than the ac Stark/Lamb shift observed in the dispersive regime using
typical circuit quantum electrodynamics devices.
