We present anisotropic transport and optical spectroscopy studies on EuCd_2As_2. The measurements reveal that EuCd_2As_2 is a low carrier density semimetal with moderate anisotropic resistivity ratio. The charge carriers experience very strong scattering from Eu magnetic moments, resulting in a Kondo-like increase of resistivity at low temperature. Below the antiferromagnetic transition temperature at $T_N$= 9.5 K, the resistivity drops sharply due to the reduced scattering from the ordered Eu moments. Nevertheless, the anisotropic ratio of $rho_c/rho_{ab}$ keeps increasing, suggesting that the antiferromagnetic coupling is along the c-axis. The optical spectroscopy measurement further reveals, besides an overdamped reflectance plasma edge at low energy, a strong coupling between phonon and electronic continuum. Our study suggests that EuCd_2As_2 is a promising candidate displaying intriguing interplay among charge, magnetism and the underlying crystal lattice.