This paper investigates the outage performance of a reconfigurable intelligent surface (RIS)-assisted communication system with statistical channel state information (CSI) over Rician fading channels. An approximate closed-form expression of the outage probability is derived by determining the distribution of the RIS-based composite channel. To obtain more insights into the system performance, we derive an asymptotic outage probability expression at high signal-to-noise ratio (SNR) region and scaling laws for the coding gain with both continuous and discrete phase shifts. Analytical and simulation results show that the diversity gain is not affected by the number of reflecting elements, but the coding gain exponentially and linearly grows with the number of reflecting elements if the Rician channel factors are larger than and equal to zero, respectively.