Programmable photonic circuits (PPCs) have garnered substantial interest in achieving deep learning accelerations and universal quantum computations. Although photonic computation using PPCs offers critical advantages, including ultrafast operation, energy-efficient matrix calculation and room-temperature quantum states, its poor scalability impedes the integration required for industrial applications. This challenge arises from the temporally one-shot operation using propagating light in conventional PPCs, which leads to the light-speed increase of device footprints. Here we propose a concept of programmable photonic time circuits, which employ time-cycle-based computations analogous to the gate cycling in the von Neumann architecture and quantum computation. As a building block, we develop a reconfigurable SU(2) time gate composed of two resonators, which have tunable resonances and are coupled through time-coded dual-channel gauge fields. We demonstrate universal U(N) operations with high fidelity using the systematic assembly of the SU(2) time gates, achieving improved scalability from O(N^2) to O(N) in both the footprint and gate number. This result opens a pathway to industrial-level PPC implementation in very large-scale integration.