Orthogonal Frequency-Division Multiplexing (OFDM) radar is receiving increasing attention in the radar field in recent years and is showing excellent performance. However, for practical applications, there are several problems with phase-coded OFDM radar, such as the existence of few good codes, limited length capability, and a high Peak-to-Mean-Envelope Power Ratio (PMEPR). To address those problems, in this paper, we propose a design method for a four-phase-coded OFDM radar signal based on Bernoulli chaos, which can construct codes of arbitrary amounts and lengths and demonstrate more agility and flexibility. By adopting original phase weighting, this method can obtain a chaotic four-phase-coded OFDM signal with a PMEPR less than two. This signal has excellent performance with respect to high resolution and Doppler radar application.