Although several thousands of exoplanets have now been detected and characterized, observational biases have led to a paucity of long-period, low-mass exoplanets with measured masses and a corresponding lag in our understanding of such planets. In this paper we report the mass estimation and characterization of the long-period exoplanet Kepler-538b. This planet orbits a Sun-like star (V=11.27) with M_=0.892-0.035_^+0.051^ M_{sun} and R=0.8717-0.0061_^+0.0064^ R_{sun}. Kepler-538b is a 2.215-0.034_^+0.040^ R_{Earth} sub-Neptune with a period of P=81.73778+/-0.00013 days. It is the only known planet in the system. We collected radial velocity (RV) observations with the High Resolution Echelle Spectrometer (HIRES) on Keck I and High Accuracy Radial velocity Planet Searcher in North hemisphere (HARPS-N) on the Telescopio Nazionale Galileo (TNG). We characterized stellar activity by a Gaussian process with a quasi-periodic kernel applied to our RV and cross-correlation function FWHM observations. By simultaneously modeling Kepler photometry, RV, and FWHM observations, we found a semi-amplitude of K=1.68-0.38_^+0.39^ m/s and a planet mass of M_p_=10.6_-2.4_^+2.5^ M_{Earth}_. Kepler-538b is the smallest planet beyond P=50 days with an RV mass measurement. The planet likely consists of a significant fraction of ices (dominated by water ice), in addition to rocks/metals, and a small amount of gas. Sophisticated modeling techniques such as those used in this paper, combined with future spectrographs with ultra high-precision and stability will be vital for yielding more mass measurements in this poorly understood exoplanet regime. This in turn will improve our understanding of the relationship between planet composition and insolation flux and how the rocky to gaseous transition depends on planetary equilibrium temperature.