We report the differential charged jet cross section and jet fragmentation distributions measured with the ALICE detector in proton-proton collisions at a center-of-mass energy √ s = 7     TeV . Jets with pseudorapidity | η | < 0.5 are reconstructed from charged particles using the anti- k T jet-finding algorithm with a resolution parameter R = 0.4 . The jet cross section is measured in the transverse momentum interval 5 ≤ p ch   jet T < 100     GeV / c . Jet fragmentation is studied measuring the scaled transverse momentum spectra of the charged constituents of jets in four intervals of jet transverse momentum between 5 and 30     GeV / c . The measurements are compared to calculations from the pythia model as well as next-to-leading-order perturbative QCD calculations with powheg+pythia8. The charged jet cross section is well described by powheg for the entire measured range of p ch   jet T . For p ch   jet T > 40     GeV / c , the pythia calculations also agree with the measured charged jet cross section. pythia6 simulations describe the fragmentation distributions to 15%. Larger discrepancies are observed for pythia8.