Whenever several antennas are brought in proximity with one another, their electromagnetic coupling gives rise to changes in their emission properties such as radiation power and resonance frequencies. These effects have a quantum counterpart in atomic physics phenomena such as super-radiance and cooperative line shifts. Here, we report a direct spectroscopic observation of the collective frequency shift of an optical electric-dipole transition in a system of up to seven Sr+ ions suspended in a Paul trap. We study cooperative line shifts in the previously unexplored regime of far-field coupling and provide the first observation of cooperative phenomena in an array of quantum emitters. These results pave the way towards experimental exploration of cooperative emission phenomena in mesoscopic systems.