The inter-strand contact resistance (R_C) of Nb₃Sn cable-in-conduit conductors (CICCs) is a very important parameter which strongly correlates with ac losses and current redistribution behavior of the CICCs. One way to obtain the desired R_C is to apply a layer of hydrocarbon oil on the Nb₃Sn strands before the CICC Nb₃Sn reaction heat treatment. In this paper, we measured R_C for a Nb₃Sn CICC sample fabricated with hydrocarbon oil. The measurements were performed using an apparatus designed to apply transverse load and load cycling on CICCs at 4.2 K. Resistances R_C between strands of different cabling stages were measured with transverse load up to 188 kN m⁻¹ and load cycles up to 10 000. The results show that R_C of the sample increases almost linearly with the first loading. With load cycling, R_C increases rapidly at first, but becomes saturated after ~100 cycles. After 10 000 load cycles, R_C decreases with increasing load at a decreasing rate. These behaviors are comparable to observations for CICC with Cr plated strands reported in the literature. Therefore from the R_C point of view, Nb₃Sn CICCs with hydrocarbon oil on strands may be used as a low cost alternative to CICCs with Cr plated strands.