Cellular-based machine-to-machine (M2M) communication is expected to facilitate services for the Internet of Things (IoT). However, because cellular networks are designed for human users, they have some limitations. Random access channel (RACH) congestion caused by massive access from M2M devices is one of the biggest factors hindering cellular-based M2M services because the RACH congestion causes random access (RA) throughput degradation and connection failures to the devices. In this paper, we show the possibility exploiting the capture effects, which have been known to have a positive impact on the wireless network system, on RA procedure for improving the RA performance of M2M devices. For this purpose, we analyze an RA procedure using a capture model. Through this analysis, we examine the effects of capture on RA performance and propose a Msg3 power-ramping (Msg3 PR) scheme to increase the capture probability (thereby increasing the RA success probability) even when severe RACH congestion problem occurs. The proposed analysis models are validated using simulations. The results show that the proposed scheme, with proper parameters, further improves the RA throughput and reduces the connection failure probability, by slightly increasing the energy consumption. Finally, we demonstrate the effects of coexistence with other RA-related scheme through simulation result.