By activating blocked users and altering successive interference cancellation (SIC) sequences, reconfigurable intelligent surfaces (RISs) become promising for enhancing non-orthogonal multiple access (NOMA) systems. This work investigates the downlink performance of RIS-aided NOMA networks via stochastic geometry. We first introduce the unique path loss model for RIS reflecting channels. Then, we evaluate the angle distributions based on a Poisson cluster process (PCP) framework, which theoretically demonstrates that the angles of incidence and reflection are uniformly distributed. Lastly, we derive closed-form expressions for coverage probabilities of the paired NOMA users. Our results show that 1) RIS-aided NOMA networks perform better than the traditional NOMA networks; 2) the SIC order in NOMA systems can be altered since RISs are able to change the channel gains of NOMA users.