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PSO J318.5338$-$22.8603 is an extremely-red planetary-mass object that hasbeen identified as a candidate member of the $\beta$ Pictoris moving groupbased on its spatial position and tangential velocity. We present a highresolution $K$-band spectrum of PSO J318.5338$-$22.8603. Using aforward-modeling Markov Chain Monte Carlo approach, we report the firstmeasurement of the radial velocity and $v$ sin($i$) of PSO J318.5$-$22,$-$6.0$^{+0.8}_{-1.1}$ km s$^{-1}$ and 17.5$^{+2.3}_{-2.8}$ km s$^{-1}$,respectively. We calculate the space velocity and position of PSO J318.5$-$22and confirm that it is a member of the $\beta$ Pictoris moving group. Adoptingan age of 23$\pm$3 Myr for PSO J318.5$-$22, we determine a mass of $8.3\pm0.5$$M_{\rm{Jup}}$ and effective temperature of $1127^{+24}_{-26}$ K usingevolutionary models. PSO J318.5338$-$22.8603 is intermediate in mass andtemperature to the directly-imaged planets $\beta$ Pictoris b and 51 Eridani b,making it an important benchmark object in the sequence of planetary-massmembers of the $\beta$ Pictoris moving group. Combining our $v$ sin($i$)measurement with recent photometric variability data, we constrain theinclination of PSO J318.5$-$22 to $>29^{\circ}$ and its rotational period to5-10.2 hours. The equatorial velocity of PSO J318.5$-$22 indicates that itsrotation is consistent with an extrapolation of the velocity-mass relationshipfor solar system planets.

The Radial and Rotational Velocities of PSO J318.5338$-$22.8603, a Newly Confirmed Planetary-Mass Member of the $\beta$ Pictoris Moving Group