Robotic continuous control tasks impose stringent demands on the energy efficiency and latency of computing architectures due to their high-dimensional state spaces and real-time interaction requirements. Conventional electronic computing platforms face computational bottlenecks, whereas the fusion of photonic computing and spiking reinforcement learning (RL) offers a promising alternative. Here, we propose a novel computing architecture based on photonic spiking RL, which integrates the Twin Delayed Deep Deterministic policy gradient (TD3) algorithm with spiking neural network (SNN). The proposed architecture employs an optical-electronic hybrid computing paradigm wherein a silicon photonic Mach-Zehnder interferometer (MZI) chip executes linear matrix computations, while nonlinear spiking activations are performed in the electronic domain. Experimental validation on the Pendulum-v1 and HalfCheetah-v2 benchmarks demonstrates the system capability for software-hardware co-inference, achieving a control policy reward of 5831 on HalfCheetah-v2, a 23.33% reduction in convergence steps, and an action deviation below 2.2%. Notably, this work represents the first application of a programmable MZI photonic computing chip to robotic continuous control tasks, attaining an energy efficiency of 1.39 TOPS/W and an ultralow computational latency of 120 ps. Such performance underscores the promise of photonic spiking RL for real-time decision-making in autonomous and industrial robotic systems.