This can easily be seen by the following argument. Consider a kinetic term in Euclidean space for a scalar field f of the form M ab@af@bf. In four dimensions M ab must be a dimensionless tensor that has hypercubic symmetry. The only such tensor is dab, so rotation invariance is automatically preserved. Interaction terms are by their very nature rotation invariant, which implies that the entire action is invariant under the full rotation group.