Convolutional operations are computationally intensive in artificial intelligence services, and their overhead in electronic hardware limits machine learning scaling. Here, we introduce a photonic joint transform correlator (pJTC) using a near-energy-free on-chip Fourier transformation to accelerate convolution operations. The pJTC reduces computational complexity for both convolution and cross-correlation from O(N4) to O(N2), where N2 is the input data size. Demonstrating functional Fourier transforms and convolution, this pJTC achieves 98.0% accuracy on an exemplary MNIST inference task. Furthermore, a wavelength-multiplexed pJTC architecture shows potential for high throughput and energy efficiency, reaching 305 TOPS/W and 40.2 TOPS/mm2, based on currently available foundry processes. An efficient, compact, and low-latency convolution accelerator promises to advance next-generation AI capabilities across edge demands, high-performance computing, and cloud services.