KA1858+4850 is a narrow-line Seyfert 1 galaxy at redshift 0.078 and is among the brightest active galaxies monitored by the Kepler mission. We have carried out a reverberation mapping campaign designed to measure the broad-line region size and estimate the mass of the black hole in this galaxy. We obtained 74 epochs of spectroscopic data using the Kast Spectrograph at the Lick 3 m telescope from 2012 February to November, and obtained complementary V-band images from five other ground-based telescopes. We measured the H{beta} light curve lag with respect to the V-band continuum light curve using both cross-correlation techniques (CCF) and continuum light curve variability modeling with the JAVELIN method and found rest-frame lags of {tau}_CCF_=13.53_-2.32_^+2.03^ days and {tau}_JAVELIN_=13.15_-1.00_^+1.08^ days. The H{beta} rms line profile has a width of {sigma}_line_=770+/-49 km/s. Combining these two results and assuming a virial scale factor of f=5.13, we obtained a virial estimate of M_BH_=8.06_-1.72_^+1.59^x10^6^M_{sun}_ for the mass of the central black hole and an Eddington ratio of L/L_Edd_{approx}0.2. We also obtained consistent but slightly shorter emission-line lags with respect to the Kepler light curve. Thanks to the Kepler mission, the light curve of KA1858+4850 has among the highest cadences and signal-to-noise ratios ever measured for an active galactic nucleus; thus, our black hole mass measurement will serve as a reference point for relations between black hole mass and continuum variability characteristics in active galactic nuclei.