To improve the decoding performance and transmission efficiency of optical communication link in atmospheric weak turbulence channel, heuristic adaptive rate polar codes were proposed. Adaptive rate polar codes were designed based on nesting property of information bits of polar codes, which could achieve fully polarization and good error-correcting performance in atmospheric weak turbulence channel. To adjust the code rate of adaptive rate polar codes, cyclic redundancy check(CRC) code was introduced as stop signs, which could check decoding result. Transmitting terminal sent a set of codes with gradually lower code rates, when the received codes passed CRC check, transmitting terminal stopped and the rate of such code was the largest rate which can ensure reliable transmission. Simulation results show that, compared to traditional polar codes, adaptive rate polar codes can obtain 1.7 dB to 2.3 dB coding gain at the frame error rate(FER) of 10-8 in different atmospheric turbulence intensity. Decoding latency of adaptive rate polar codes was simulated and the throughput rate of adaptive rate polar codes was calculated. The results show that adaptive rate polar codes can meet the transmission requirements of FSO in atmospheric weak turbulence channel.