We report low-temperature magnetoresistance (MR) measurements on rings of single-wall carbon nanotubes. Negative MR characteristic of weak one-dimensional localization is clearly observed from 3.0 to 60 K, and the coherence length Lφ is obtained as a function of temperature. The dominant dephasing mechanism is identified as electron-electron scattering. Below 1 K, we observe a transition from weak to strong localization, and below 0.7 K a weak antilocalization is induced by spin-orbit scattering..