We propose a scheme to engineer a non-local two-qubit phase gate between two remote quantum-dot spins.Along with one-qubit local operations,one can in principal perform various types of distributed quantum information processing.The scheme employs a photon with linearly polarisation interacting one after the other with two remote quantum-dot spins in cavities.Due to the optical spin selection rule,the photon obtains a Faraday rotation after the interaction process.By measuring the polarisation of the final output photon,a non-local two-qubit phase gate between the two remote quantum-dot spins is constituted.Our scheme may has very important applications in the distributed quantum information processing. We propose a scheme to engineer a non-local two-qubit phase gate between two remote quantum-dot spins. With one-qubit local operations, one can in principal perform various types of distributed quantum information information. The scheme employs a photon with linearly polarisation interacting one after the other with two remote quantum-dot spins in cavities. Due to the optical spin selection rule, the photon obtaining a Faraday rotation after the interaction process.By measuring the polarisation of the final output photon, a non-local two-qubit phase gate between the two remote quantum-dot spins is composed. Our scheme may have very important applications in the distributed quantum information processing.