The scattering and absorption of an obliquely incident, plane electromagnetic wave by an infinite, cylindrically symmetrical region characterizable by a complex dielectric ``constant'' is determined by application of the Born approximation for the case of dielectric ``constant'' near unity. Differential‐scattering cross sections and absorption cross sections are derived as a function of angle of incidence, angle of polarization, and integrals over the inhomogeneous region. The expressions for the scattered fields are compared to the expansion of an exact solution for the homogeneous dielectric cylinder in the limit of dielectric constant near unity. The approximate expressions agree exactly. Of singular notability in this respect is the fact that polarization is altered in the Born approximation by the appearance of dyadic terms in the propagation equation in the region of inhomogeneity, while the exact solution requires the generation of cross‐polarized waves to satisfy boundary conditions.