Analysis of geostatistical data is often based on the assumption that the spatial random field is isotropic. This assumption, if erroneous, can adversely affect model predictions and statistical inference. Nowadays since applications consider data over the globe, it is necessary to check the assumption of isotropy on a sphere. In this paper, a test for spatial isotropy on a sphere is proposed. The data are first projected onto the set of spherical harmonic functions. Under isotropy, the spherical harmonic coefficients are uncorrelated whereas they are correlated if the fields are not isotropic. This motivates a test based on the sample correlation matrix of the spherical harmonic coefficients. Extensive simulations are conducted to assess the Type I errors of the test under different scenarios. We show how temporal correlation affects the test and provide a method for handling temporal correlation. We also gauge the power of the test as we move away from isotropy. The method is applied to air temperature data which is part of the HadCM3 model output. We propose some anisotropic models and apply the test to the isotropic parts to determine how well the models capture the scenarios.