Quantum wires subject to the combined action of spin-orbit and Zeeman coupling in the presence of emph{s}-wave pairing potentials (superconducting proximity effect in semiconductors or superfluidity in cold atoms) are one of the most promising systems for the developing of topological phases hosting Majorana fermions. The breaking of time-reversal symmetry is essential for the appearance of unpaired Majorana fermions. By implementing a emph{time-dependent} spin rotation, we show that the standard magnetostatic model maps into a emph{non-magnetic} one where the breaking of time-reversal symmetry is guaranteed by a periodical change of the spin-orbit coupling axis as a function of time. This suggests the possibility of developing the topological superconducting state of matter driven by external forces in the absence of magnetic fields and magnetic elements. From a practical viewpoint, the scheme avoids the disadvantages of conjugating magnetism and superconductivity, even though the need of a high-frequency driving of spin-orbit coupling may represent a technological challenge. We describe the basic properties of this Floquet system by showing that finite samples host unpaired Majorana fermions at their edges despite the fact that the bulk Floquet quasienergies are gapless and that the Hamiltonian at each instant of time preserves time-reversal symmetry. Remarkably, we identify the mean energy of the Floquet states as a topological indicator. We additionally show that the localized Floquet Majorana fermions are robust under local perturbations. Our results are supported by complementary numerical Floquet simulations.
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