Authors:Lopez-Morales et alAbstract:HD 179070, aka Kepler-21, is a V = 8.25 F6IV star and the brightest exoplanet host discovered by Kepler. An early detailed analysis by Howell et al. (2012) of the first thirteen months (Q0 - Q5) of Kepler light curves revealed transits of a planetary companion, Kepler-21b, with a radius of about 1.60 +/- 0.04 R_earth and an orbital period of about 2.7857 days. However, they could not determine the mass of the planet from the initial radial velocity observations with Keck-HIRES, and were only able to impose a 2-sigma upper limit of 10 M_earth. Here we present results from the analysis of 82 new radial velocity observations of this system obtained with HARPS-N, together with the existing 14 HIRES data points. We detect the Doppler signal of Kepler-21b with a radial velocity semi-amplitude K = 2.00 +/- 0.65 m/s, which corresponds to a planetary mass of 5.1 +/- 1.7 M_earth. We also measure an improved radius for the planet of 1.639 (+0.019, -0.015) R_earth, in agreement with the radius reported by Howell et al. (2012). We conclude that Kepler-21b, with a density of 6.4 +/- 2.1 g/cm^3, belongs to the population of terrestrial planets with iron, magnesium silicate interiors, which have lost the majority of their envelope volatiles via stellar winds or gravitational escape. The radial velocity analysis presented in this paper serves as example of the type of analysis that will be necessary to confirm the masses of TESS small planet candidates.