A SQUID current sensor with integrated input coil is designed and fabricated using our new technology with Nb-AlOx-Nb cross-type Josephson junctions. The white noise level of the SQUID was measured to be of 1 µ0/Hz1/2 corresponding to current resolution of about 110 fA/Hz1/2. A superconducting transformer with a turn ratio of 19:1 was fabricated in our standard Nb technology. The transformer chip size is 12.5 mm x 12.5 mm. Three transformer chips were assembled in flip-chip configuration yielding an effective ratio of turns of 48:1. The current sensor SQUID with this transformer at the input has a current sensitivity of 4.1 nA/0. The second stage SQUID amplifier was used to characterize the noise performance of the current sensor SQUID. The measured noise level of the current sensor corresponds to the noise limited current resolution of 3 fA/Hz1/2 in white noise region and at 100 Hz and 10 Hz it is lower than 5 fA/Hz1/2 and 10 fA/Hz1/2, respectively.