What is his prescription? Actually, your son should choose swimming goggles with degrees 50 ~ 100 lower than usual, because there is light refraction in the water, and the distance between the goggles and the eyes is closer than frame glasses.
Of course he can, swimming goggles also have prescription thus you can choose them for your son, but the degree should be around 50 lower, and the lenses must be high quality.
Actually, he should wear them, because the water of swimming pool is not very clean which may even cause bacterial infection. You should pay attention to the eye health that the swimming goggles can protect his eyes from bacteria.