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Ongoing, extreme-precision Doppler radial velocity surveys seek planets with masses less than several M$_\oplus$; population-level studies to determine the distribution of planetary masses, however, remain difficult due to the required observational time investment, as well as challenges associated with robustly detecting the lowest mass planets. We outline a novel approach that leverages extensive, existing RV datasets to constrain masses of exoplanet populations: stacking periodograms of RV timeseries across many targets. We show that an exoplanet population may be statistically identifiable in the stacked periodogram, even when individual planets do not pass the threshold of detection. We discuss analytical, statistical properties of the stacked periodogram, perform simulations to demonstrate the efficacy of the method, and investigate the influence of semi-structured window functions and stellar activity. Analysis of the Lick-Carnegie Exoplanet Survey data set reveals a marginally significant ($1.6σ$) signal consistent with a population of exoplanets occupying $3-7$ day periods with typical $K$ between $1.6-5.1$ m s$^{-1}$. More detailed investigation of signals associated with stellar activity and yearly systematics may be necessary to confirm this result or detect other underlying Keplerian contributions.