We theoretically investigate loop currents generated by a Berry phase that arises from spin vortices and argue that a coherent collection of them forms a supercurrent in cuprate superconductors. First, we explain enhanced Nernst signals in cuprates using a fictitious electric field that arises from flow of spin vortices with their centers at sites where lattice-distortion-clad holes (small polaronic holes) reside. Assuming the coexistence of holes in large and small polaron forms, the magnitude of the Nernst signal is shown to be proportional to density and mobility of small polarons, and expressed as e(N) = c(3)T(-1)e(-0.51Wp/kBT)/(1 + (2 pi m*k(B)T)/(n(s)h(2))e(-Wp/kBT)), where c(3) is a constant, W-p is the small polaron formation energy, n(s) is the surface density of sites, and m* is the effective mass of the large polaron; by treating unknown parameters as fitting parameters, this formula follows the experimental temperature dependence very well. From the obtained W-p value, it is indicated that superconductivity occurs at temperatures where almost all of the holes become small polarons; thus, the conventional current generation mechanism is ineffective at temperatures around T-c; however, loop current generation by the spin Berry phase is effective. We calculate the superconducting transition temperature as an order-disorder transition temperature of the loop currents. The doped hole concentration, x, dependence of the transition temperature is obtained as T-c = T-0 ln x/x(0) and agrees with experimental data, where T-0 and x(0) are treated as fitting parameters. Lastly, we briefly mention an artificial nanostructure that generates a persistent current by utilizing the spin Berry phase.