Sure.  I have no idea what an efficient algorithm looks like, but since you only asked whether it's possible I'll offer a terrible one.  Use <a href="http://en.wikipedia.org/wiki/Rouch%C3%A9%27s_theorem">Rouche's theorem</a> to find $R$ such that all roots lie within a disk of radius $R$ centered at the origin, then subdivide the disk into, say, a mesh of squares of side length $\epsilon > 0$ and evaluate the polynomial at all the lattice points of the mesh.  As the mesh size tends to zero you'll find points that approximate the zeroes to arbitrary accuracy.