Recent breakthroughs in electrical detection and manipulation of antiferromagnets have opened a new avenue in the research of non-volatile spintronic devices. Antiparallel spin sublattices in antiferromagnets, producing zero dipolar fields, lead to the insensitivity to magnetic field perturbations, multi-level stability, ultra-fast spin dynamics and other favorable characteristics which may find utility in fields ranging from magnetic memories to optical signal processing. However, the absence of a net magnetic moment and the ultra-short magnetization dynamics timescales make antiferromagnets notoriously difficult to study by common magnetometers or magnetic resonance techniques. In this paper we demonstrate the experimental determination of the Neel vector in a thin film of antiferromagnetic CuMnAs which is the prominent material used in the first realization of antiferromagnetic memory chips. We employ a femtosecond pump-probe magneto-optical experiment based on magnetic linear dichroism. This table-top optical method is considerably more accessible than the traditionally employed large scale facility techniques like neutron diffraction and X-ray magnetic dichroism measurements. This optical technique allows an unambiguous direct determination of the Neel vector orientation in thin antiferromagnetic films utilized in devices directly from measured data without fitting to a theoretical model.