We present the [C II] 158 mu m line luminosity functions (LFs) at z similar to 4-6 using the ALMA observations of 118 sources, which are selected to have UV luminosity M-1500A < -20.2 and optical spectroscopic redshifts in COSMOS and ECDF-S. Of the 118 targets, 75 have significant [C II] detections and 43 are upper limits. This is by far the largest sample of [C II] detections, which allows us to set constraints on the volume density of [C II] emitters at z similar to 4-6. But because this is a UV-selected sample, we are missing [C II]-bright but UV-faint sources, making our constraints strict lower limits. Our derived LFs are statistically consistent with the z similar to 0 [C II] LF at 10(8.25)-10(9.75)L. We compare our results with the upper limits of the [C II] LF derived from serendipitous sources in the ALPINE maps. We also infer the [C II] LFs based on published far-IR and CO LFs at z similar to 4-6. Combining our robust lower limits with these additional estimates, we set further constraints on the true number density of [C II] emitters at z similar to 4-6. These additional LF estimates are largely above our LF at L-[CII] > 10(9)L, suggesting that UV-faint but [C II]-bright sources likely make significant contributions to the [C II] emitter volume density. When we include all the LF estimates, we find that available model predictions underestimate the number densities of [C II] emitters at z similar to 4-6. Finally, we set a constraint on the molecular gas mass density at z similar to 4-6, with rho(mol) similar to (2-7) x 10(7)M Mpc(-3). This is broadly consistent with previous studies.