Sco X-1 is the brightest persistent X-ray source in the sky. It is generally believed that Sco X-1 is a low-mass X-ray binary containing a neutron star that accretes from a low-mass donor star where the mass transfer is driven by magnetic braking. However, the mass transfer rate predicted by the standard magnetic braking model is at least one order of magnitude lower than the rate inferred by X-ray luminosity. In this work, we investigate whether this source could have evolved from an intermediate-mass X-ray binary including Ap/Bp stars with a slightly strong magnetic field of 300 -1000 G. The coupling between the magnetic field and an irradiation-driven wind induced by the X-ray flux from the accretor can yield strong magnetic braking that could give rise to a relatively high mass transfer rate. According to the observed orbital period, the mass transfer rate, the mass ratio, and the donor star spectral type, the progenitor of Sco X-1 should be an intermediate-mass X-ray binary including a 1.6 − 1.8 M ⊙ Ap/Bp donor star in a 1.3 − 1.5 day orbit. We therefore propose that anomalous magnetic braking of Ap/Bp stars provides an alternative evolutionary channel to some of the luminous X-ray sources.