We present size measurements of 78 high-redshift (z => 5.5) galaxy candidates from the Reionization Lensing Cluster Survey (RELICS). These distant galaxies are well resolved due to the gravitational lensing power of foreground galaxy clusters, imaged by the Hubble Space Telescope and the Spitzer Space Telescope. We compute sizes using the forward-modelling code lenstruction and account for magnification using public lens models. The resulting size-magnitude measurements confirm the existence of many small galaxies with effective radii R_eff_ < 200 pc in the early Universe, in agreement with previous studies. In addition, we highlight compact and highly star-forming sources with star formation rate surface densities {Sigma}_SFR_ > 10M_{sun}_yr^-1^kpc^-2^ as possible Lyman continuum leaking candidates that could be major contributors to the process of reionization. Future spectroscopic follow-up of these compact galaxies (e.g. with the James Webb Space Telescope) will further clarify their role in reionization and the physics of early star formation.