An exact, axially symmetric solution to the Einstein-Klein-Gordon field equ
ations is employed to model the dark matter in spiral galaxies. The extende
d rotation curves from a previous analysis are used to fit the model and a
very good agreement is found. It is argued that, although our model possess
es three parameters to be fitted, it is better than the non-relativistic al
ternatives in the sense that it is not of a phenomenological nature, since
the dark matter would consist entirely of a scalar field.