We study how $d$-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a $d+id$ pairing, which arises from the chiral spin coupling and the three-site term generated by the CPL. The latter effect remains significant even for low frequencies and low intensities of the CPL. This is clearly seen in the obtained phase diagram against the laser intensity and temperature for various frequencies red-detuned from the Hubbard $U$, with the transient dynamics also examined. The phenomenon revealed here can provide a novel way to induce a topological superconductivity.
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