We propose an unsupervised variational acoustic clustering model for clustering audio data in the time-frequency domain. The model leverages variational inference, extended to an autoencoder framework, with a Gaussian mixture model as a prior for the latent space. Specifically designed for audio applications, we introduce a convolutional-recurrent variational autoencoder optimized for efficient time-frequency processing. Our experimental results considering a spoken digits dataset demonstrate a significant improvement in accuracy and clustering performance compared to traditional methods, showcasing the model's enhanced ability to capture complex audio patterns.