The cross section of jets reconstructed from charged particles is measured in the transverse momentum range of 5<pT<100 GeV/c in pp collisions at the center-of-mass energy of s=5.02 TeV with the ALICE detector. The jets are reconstructed using the anti-kT algorithm with resolution parameters R=0.2, 0.3, 0.4, and 0.6 in the pseudorapidity range |η|<0.9-R. The charged jet cross sections are compared with the leading-order (LO) and to next-To-leading-order (NLO) perturbative quantum chromodynamics (pQCD) calculations. It is found that the NLO calculations agree better with the measurements. The cross section ratios for different resolution parameters are also measured. These ratios increase from low pT to high pT and saturate at high pT, indicating that jet collimation is larger at high pT than at low pT. These results provide a precision test of pQCD predictions and serve as a baseline for the measurement in Pb-Pb collisions at the same energy to quantify the effects of the hot and dense medium created in heavy-ion collisions at the LHC.