We report on detailed magnetic investigations of big Rb3C60 single crystals with sizes of ~1 mm. The Rb3C60 crystals were prepared by doping C60 crystals in rubidium vapor. Experiments with different annealing times and various annealing temperatures and temperature gradients were made to assess the optimal conditions for homogeneous doping. The crystals were characterized by ac magnetization measurements. Doping at 463 K with 10% excess of rubidium and annealing at 685 K for 27 days was found to produce the best crystals with almost 100% of the pure Rb3C60 phase. The temperature dependence of the upper and lower critical fields was obtained, the latter by the trapped magnetic moment method. The coherence length and the penetration depth at T=0 and close to the transition temperature were evaluated and the irreversibility line was determined. The results are compared to those obtained on powder and polycrystalline samples.