We report the generation of entanglement between two individual 87Rb atoms in hyperfine ground states |F=1,M=1> and |F=2,M=2> which are held in two optical tweezers separated by 4 $\mu$m. Our scheme relies on the Rydberg blockade effect which prevents the simultaneous excitation of the two atoms to a Rydberg state. The entangled state is generated in about 200 ns using pulsed two-photon excitation. We quantify the entanglement by applying global Raman rotations on both atoms. Correcting for losses we measure a fidelity of 0.75 with respect to the target state.