Effects of rotary oscillation on unsteady laminar flow past a circular cylinder have been investigated in this study. Numerical simulations are performed for the flow at Re=100 in the range of 0.2<$Omega$<2.5 and 0.02<$St_f$<0.8, where $Omega$ and $St_f$ are, respectively, the maximum rotation velocity and rotation frequency normalized by the free-stream velocity and cylinder diameter. Results show that rotary oscillation has significant effects on the flow. When the rotation frequency is near the natural vortex-shedding frequency, lock-on occurs and the lock-on frequency range becomes wider as the rotation velocity increases. In a certain range of the rotation frequency and velocity, modulations in the velocity, lift and drag signals occur and this modulation frequency is expressed as a linear combination of the rotation frequency and vortex-shedding frequency. The mean drag and amplitude of the lift fluctuations show local minima near the boundary between the lock-on non and lock-on regions.