We report on Co K-edge x-ray magnetic circular dichroism (XMCD) measurements of LaCoO₃ single crystal in temperature range from 5 to 300 K and external magnetic field of 17 T. The response consists of pre-edge (at 7712 eV) and bi-polar peak (up at 7727, down at 7731 eV) with amplitudes, respectively, less than 10⁻³ and 10⁻² of the Co K-edge jump. Using the sum rule the orbital magnetic moment of 4p Co is evaluated. Its temperature dependence reaches a maximum of (2.7 ± 0.9) x10⁻³ μB at 120 K, following the trend for the total magnetic moment on the Co obtained from the superconducting quantum interference device measurements. However, on warming from 25 to 120 K, the orbital magnetic moment of the 4p Co doubles while total magnetic moment of Co increases 10 times. First principle calculations are in order to relate the Co K-edge XMCD results to the orbital and spin moment of 3d Co.