In the current study, a rate-dependent crystal plasticity finite element method (CPFEM) was used to simulate flow stress behavior and texture evolution of a body-centered cubic (BCC) crystalline material during plastic deformation at room temperature. To account for crystallographic slip and rotation, a rate-dependent crystal constitutive law with a hardening model was incorporated into an in-house finite element program, CAMPform3D. Microstructural heterogeneity and anisotropy were handled by assigning a crystallographic orientation to each integration point of the element and determining the stiffness matrix of the individual crystal. Uniaxial tensile tests of single crystals with different crystallographic orientations were simulated to determine the material parameters in the hardening model. The texture evolution during four different deformation modes - uniaxial tension, uniaxial compression, channel die compression, and simple shear deformation - was investigated based on the comparison with experimental data available in the literature.