The electronic and magnetic properties of a material can be altered by strain engineering. We elucidate the strain dependence of electronic and magnetic properties in alpha-RuCl3 monolayer by varying the biaxial in-plane tensile strain from 1% to 8%. The magnetic ground state of the alpha-RuCl3 monolayer evolves from antiferromagnetic zigzag (AFM-ZZ) configuration to ferromagnetic (FM) under a biaxial in-plane tensile strain higher than 2%. In a strain-free state, the FM configuration has a direct bandgap of 0.54 eV, and the AFM-ZZ configuration has an indirect bandgap of 0.73 eV. The energy bandgap of the alpha-RuCl3 monolayer undergoes a change by the variation of the tensile strain. Furthermore, a detailed Monte Carlo simulation has been implemented to investigate the magnetic properties of the considered system for varying values of tensile strain. Temperature dependencies of the thermodynamic quantities of interest as functions of strains display strong evidence supporting the first-principles calculations within density functional theory. Our Monte Carlo findings also suggest that the Curie temperature of the alpha-RuCl3 monolayer tends to get higher up to 20.11 K with a tensile strain 8%, which means that applying a strain leads to getting a more stable FM ground state. In addition, we find that magnetocrystalline anisotropy in the alpha-RuCl3 monolayer can be controlled by the applied strain.