We calculate the degree of linear polarization of radiation from stars having planets that may not be resolved spatially. We assume single scattering by water and silicate particulates in the planetary atmosphere. The dilution of the reflected polarized radiation of the planet by the unpolarized stellar radiation and the effect of oblateness of the planet as well as its elliptical orbit are included. We employ a chemical equilibrium model to estimate the number density of water and silicate condensates and calculate the degree of linear polarization at R band of starlight as a function of (1) mean size of condensates, (2) planetary oblateness, (3) inclination angle, (4) phase angle, (5) orbital eccentricity e and (6) the epoch of periastron passage. We show that the polarization profile alters significantly at all inclination angles when elliptical orbit is considered and the degree of polarization peaks at the epoch of periastron passage. We predict that detectable amount of linear polarization may arise if the planetary atmosphere is optically thin, the mean size of the condensates is not greater than a few microns and the oblateness of the planet is as high as that of Jupiter.

19 pages including 7 postscript figures, Latex (AASTEX style), Accepted for publication by The Astrophysical Journal