Private set intersection (PSI) is a hot topic in the privacy-preserving computation, which allows two parties computing the intersection of their sets without revealing any additional information except the resulting intersection. Prior PSI protocols mostly considers the scenario between two parties with the potential limitation of requiring expensive hardware. In addition, the weak client with low computation capability cannot outsource the computation to semi-trusted cloud without keeping the data privacy. This study designs a new oblivious two-party distributed pseudorandom function (Otd-PRF), which allows the semi-trusted cloud servers participating the equality test without any leakage of the set information. Based on Otd-PRF, a cloud-aided PSI protocol is designed which can delegate the major computation to the semi-trusted cloud. A formal security analysis is also provided in the semi-honest model and it is extended to support the computation of the private set intersection cardinality. Through the comparison with the related work, the proposed protocol is superior in the computation and communication complexity. This protocol is linear in the size of the client's set. Its performance analysis shows that the protocol is more friendly to the client with constrained device in the semi-honest model.