We present a particle-in-cell (PIC) method using a nonhomogeneous immersed-finite-element (IFE) field solver for modeling dielectric surface charging of complex-shaped objects in plasmas. The IFE solver allows PIC codes using a Cartesian mesh applied to simulations involving arbitrarily shaped objects with a similar accuracy as that using a body-fitting mesh. The object surface is treated as an interface. Surface charging is calculated directly from charge deposition at the interface, and the electrostatic fields on both sides of the interface are resolved self-consistently. The capability of the nonhomogeneous IFE-PIC method is demonstrated by a simulation study of the charging of an irregular-shaped asteroid in the solar wind.