We investigated temperature, field, and field-orientation dependences of the specific heat of CeIrIn5. The upper critical field H-c2 was determined down to 80 mK from the specific heat measurements and exhibits a slight suppression at low temperatures. We revealed that the specific heat at 80 mK increases proportional to the square root of H up to nearly H-c2 for both H parallel to ab and H parallel to c, implying the presence of line nodes and a weak contribution of the Pauli paramagnetic pair-breaking effect. Furthermore, we revealed that the specific heat shows a fourfold oscillation under a rotating magnetic field in the ab plane. This result indicates that CeIrIn5 has fourfold symmetry around the c axis in its gap amplitude.