An efficient algorithm for the construction of polar codes for higher-order modulation is presented based on information-theoretic principles. The bit reliabilities after successive demapping are estimated using the LM-rate, an achievable rate for mismatched decoding. The successive demapper bit channels are then replaced by binary input Additive White Gaussian Noise (biAWGN) surrogate channels and polar codes are constructed using the Gaussian approximation (GA). This LM-rate Demapper GA (LM-DGA) construction is used to construct polar codes for several demapping strategies proposed in literature. For all considered demappers, the LM-DGA constructed polar codes have the same performance as polar codes constructed by Monte Carlo (MC) simulation. The proposed LM-DGA construction is much faster than the MC construction. For 64-QAM, spectral efficiency 3 bits/s/Hz, and block length 1536 bits, simulation results show that LM-DGA constructed polar codes with cyclic redundancy check and successive cancellation list decoding are 1 dB more power efficient than state-of-the-art AR4JA low-density parity-check codes.