Learning-based probabilistic models can be combined with an entropy coder for data compression. However, due to the high complexity of learning-based models, their practical application as text compressors has been largely overlooked. To address this issue, our work focuses on a low-complexity design while maintaining compression performance. We introduce a novel Learned Lossless Low-complexity Text Compression method (L3TC). Specifically, we conduct extensive experiments demonstrating that RWKV models achieve the fastest decoding speed with a moderate compression ratio, making it the most suitable backbone for our method. Second, we propose an outlier-aware tokenizer that uses a limited vocabulary to cover frequent tokens while allowing outliers to bypass the prediction and encoding. Third, we propose a novel high-rank reparameterization strategy that enhances the learning capability during training without increasing complexity during inference. Experimental results validate that our method achieves 48% bit saving compared to gzip compressor. Besides, L3TC offers compression performance comparable to other learned compressors, with a 50x reduction in model parameters. More importantly, L3TC is the fastest among all learned compressors, providing real-time decoding speeds up to megabytes per second. Our code is available at https://github.com/alipay/L3TC-leveraging-rwkv-for-learned-lossless-low-complexity-text-compression.git.