The intermolecular potential energy surface for the van der Waals complex between helium and the CO+ cation in its 2S+ ground state has been studied by means of the coupled cluster CCSD(T) method and the series of aug-cc-pVXZ (X=D,T,Q,5) basis sets. This complex is of interest for collisions in interstellar clouds, where CO+ is known to be present, and for studies of ion mobility and the formation of mixed charged clusters in traps and drift tubes. The counterpoise procedure of Boys and Bernardi and extrapolations to infinite basis size have been used to assess the residual effects of the basis set superposition error (BSSE) on the shape of the surface and in particular on the dissociation energy and the electronic equilibrium geometry. The equilibrium structure of HeCO+ is found to be nonlinear, with the Jacobi vector enclosing an angle of ca. 45o with the C-O distance vector. The complete basis set limit for the vibrationless CCSD(T) binding energy is estimated to be about 275 cm−1. Rovibrational states and spectra of the system He-CO+ are predicted on the basis of this high level ab initio potential energy surface by a numerically exact method based on a discrete variable representation. The complex is found to belong to the class of quasi-linear molecules and indications for a low energy orbiting resonance have been found.