Corporate social responsibility (CSR) has become the focus of the company’s daily operations and strategic choices. At present, the supply risk events caused by the CSR violations of service providers in the service supply chain are frequent, which highlight the importance of formulating appropriate contracts to constrain the CSR level of providers. In the context of asymmetric CSR cost information, this paper analyzes the optimal contract parameters of integrators when providing screening contracts or pooling contracts and compares their impact on profits and the CSR level. The information asymmetry belongs to classic principal-agent problem, and we will use the revelation principle to design the contracts and solve this problem. The results that different contracts have different effects on the CSR level of different types of providers. A low-cost provider’s CSR level is the highest when a screening contract is provided, while a high-cost provider’s CSR level reaches the peak under a pooling contract. If pursuing profit maximization, the integrator should choose to provide a screening contract. When the integrator needs to ensure a higher average level of social responsibility, a pooling contract should be chosen. The findings also show that service cost is an important factor affecting the CSR level of the provider, and only when the providers’ service cost is low, will providers actively fulfill their social responsibility.