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Multiple-input multiple-output and orthogonal frequency-division multiplexing (MIMO-OFDM) are the key technologies in 4G and subsequent wireless communication systems. Conventionally, the MIMO-OFDM receiver is performed by multiple cascaded blocks with different functions and the algorithm in each block is designed based on ideal assumptions of wireless channel distributions. However, these assumptions may fail in practical complex wireless environments. The deep learning (DL) method has the ability to capture key features from complex and huge data. In this paper, a novel end-to-end MIMO-OFDM receiver framework based on \textit{transformer}, named SigT, is proposed. By regarding the signal received from each antenna as a token of the transformer, the spatial correlation of different antennas can be learned and the critical zero-shot problem can be mitigated. Furthermore, the proposed SigT framework can work well without the inserted pilots, which improves the useful data transmission efficiency. Experiment results show that SigT achieves much higher performance in terms of signal recovery accuracy than benchmark methods, even in a low SNR environment or with a small number of training samples. Code is available at https://github.com/SigTransformer/SigT.