The photofragmentation spectrum of the weakly bound Sr+ Ar is measured over the 418-448 nm wavelength region, Two vibrational progressions are observed and are attributed to transitions from the X(2) Sigma(1/2) electronic ground state to vibrational levels of the excited A (II1/2)-I-2 and A (II3/2)-I-2 states, Isotope-resolved measurements of several of the observed transitions are performed to obtain the absolute vibrational numbering. From these, the spectroscopic constants of the involved states are deduced. We obtain omega(e)’ = 120.8 cm(-1), omega(e) chi(e)’ = 1.67 cm(-1), and D-0’ = 2303+/-232 cm(-1) for the A (II1/2)-I-2 state and omega(e)’ = 122 cm(-1), omega(e) chi(e)’ = 1.6 cm(-1), and D-0’, = 2575+/-256 cm(-1) for the A (II3/2)-I-2 state. For the ground X (2) Sigma(1/2) state the observed hot bands yield Delta G(1/2)" = 48 cm(-1). Furthermore a value of 803+/-244 cm(-1) is estimated for D-0 ". Finally the potential constants are compared with pseudopotential calculations from literature and the trends of binding energies for group II cation-argon complexes are discussed.