Four 3rd order fiber Bragg gratings were inscribed into separate cores of a 7 core multi-core fiber using the point-by-point inscription technique. A 1030 nm, 206 ± 5 fs laser was used, operating at a frequency of 1 kHz and pulse energy of 2.1 ± 0.2 µJ. Independent Bragg resonances at λB = 1541.01 ± 0.02, 1547.82 ± 0.02, 1532.66 ± 0.02, and 1537.42 ± 0.02 nm and extinction ratios of 13.97 ± 0.4, 16.02 ± 0.4, 10.08 ± 0.4 and 13.40 ± 0.4 dB were recorded. Our data analysis shows that refractive index changes, Δn, of the order 10-3 were induced. Core-specific inscription of fiber Bragg gratings in a multi-core fiber can provide a flexible and versatile platform to address the needs of recent space division multiplexed transmission and optical sensor networks.