Regional Short Message Communication (RSMC) service of BeiDou Navigation Satellite System (BDS) has been widely used in various fields. BDS-3 officially started to provide service in 2020, and the performance of RSMC service was greatly improved, which offers an opportunity for large-scale applications of RSMC in consumer electronic products. Due to the complex application scenarios, the low-cost and low-power of RSMC terminals, a better coding scheme is needed to improve performance. In this paper, we propose a new polar encoding scheme with low code rate and variable code length, which adopts Polarization Weight (PW) to generate the reliability sequence of Polar codes and use a Nested Rate Adaptation Sequence (NRAS) to realize rate adaption for the BDS-3 RSMC. The performance of encoding gain and decoding complexity is analyzed by simulation and experiments. The results validate the effective of this scheme. Compared with Turbo codes, the proposed polar codes scheme achieves about 0.5dB gain with about 50% decoding complexity when the information length including CRC is 128 and code rate is 1/2. The proposed polar codes scheme provides a good reference for further applications in BDS.