We propose a scheme to create electronic Floquet vortex states by irradiating the circularly-polarized laser light carrying non-zero orbital angular momentum on the two-dimensional semiconductor. We study the properties of the Floquet vortex states analytically and numerically using methods analogous to the techniques used for the analysis of superconducting vortex states, while we exhibit that the Floquet vortex created in the current system has the wider tunability. To illustrate the impact of such tunability in quantum engineering, we demonstrate how these vortex states can be used for quantum information processing. Following these findings and using numerical results for wave functions and energy dispersions, we calculate the frequency-dependent optical longitudinal and Hall conductivities via Kubo formalism.