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Cd₃As₂ is a 3D topological Dirac semimetal with non-trivial Fermi-arc surface states. It has been suggested that topological superconductivity can be achieved in the Fermi arcs by utilizing the superconducting proximity effect. Here we report a series of first observations of supercurrent states in Al-Cd₃As₂-Al Josephson junctions. First, the junction reaches a zero-resistance state at temperatures below 0.8K. Second, a non-monotonic B-field dependence is observed for the critical current I_c, where I_c is at first enhanced by increasing magnetic fields. In one sample, I_c increases from 4.6μA at B=0 to 4.8μA at B=5mT and further increasing the B field to 40mT eventually quenches I_c. Third, I_c exhibits a weak π-periodic Josephson effect at a temperature below 0.2K. Finally, Shapiro steps are also observed in a.c. Josephson effect measurements. Taken together, our results suggest that an unconventional electronic state is realized in the proximity-induced superconducting Cd₃As₂.