We present a calculation of the low-energy phase shift and scattering length for the strontium atom, using the Dirac-Coulomb Hamiltonian augmented with a model polarization potential. The scattering length is extracted from the asymptotic behavior of the wave function in the zero-energy limit. To evaluate the reliability of our results, we compare them with existing experimental data and previous theoretical predictions. Bound-state properties are obtained using a multiconfigurational approach with the GRASP2018 package, while continuum states are computed with a modified version of the GRASP code, known as GRASPC, recently published in Computer Physics Communications.