HD 179070 , { \it aka } Kepler-21 , is a { V } = 8.25 F6IV star and the brightest exoplanet host discovered by { \it Kepler } . An early detailed analysis by ( 34 ) of the first thirteen months ( Q0 – Q5 ) of { \it Kepler } light curves revealed transits of a planetary companion , Kepler-21b , with a radius of about 1.60 \pm 0.04 { R _ { \oplus } } 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 \pm 0.65 { m~ { } s ^ { -1 } } , which corresponds to a planetary mass of 5.1 \pm 1.7 M _ { \oplus } . We also measure an improved radius for the planet of 1.639 ^ { +0.019 } _ { -0.015 } R _ { \oplus } , in agreement with the radius reported by ( 34 ) . We conclude that Kepler-21b , with a density of 6.4 \pm 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 .