Free-space optical communication is a promising means to establish versatile, secure and high-bandwidth communication between mobile nodes for many critical applications. While the spatial modes of light offer a degree of freedom to increase the information capacity of an optical link, atmospheric turbulence can introduce severe distortion to the spatial modes and lead to data degradation. Here, we demonstrate experimentally a vector-beam-based, turbulence-resilient communication protocol, namely spatial polarization differential phase shift keying (SPDPSK), that can reliably transmit high-dimensional information through a turbulent channel without the need of any adaptive optics for beam compensation. In a proof-of-principle experiment with a controllable turbulence cell, we measure a channel capacity of 4.84 bits per pulse using 34 vector modes through a turbulent channel with a scintillation index of 1.09, and 4.02 bits per pulse using 18 vector modes through even stronger turbulence corresponding to a scintillation index of 1.54.