  Geometric gates that use the global property of the geometric phase is
believed to be a powerful tool to realize fault-tolerant quantum computation.
However, for singlet-triplet qubits in semiconductor quantum dot, the low Rabi
frequency of the microwave control leads to overly long gating time, and thus
the constructing geometric gate suffers more from the decoherence effect. Here
we investigate the key issue of whether the fast geometric gate can be realized
for singlet-triplet qubits without introducing an extra microwave-driven pulse,
while maintaining the high-fidelity gate operation at the same time. We
surprisingly find that both the single- and two-qubit geometric gates can be
implemented via only modulating the time-dependent exchange interaction of the
Hamiltonian, which can typically be on the order of $\sim$GHz, and thus the
corresponding gate time is of several nanoseconds. Furthermore, the obtained
geometric gates are superior to their counterparts, i.e., the conventional
dynamical gates for singlet-triplet qubits, with a relatively high fidelity
surpassing $99\%$. Therefore our scheme is particularly applied to
singlet-triplet qubits to obtain fast and high-fidelity geometric gates. Our
scheme can also be extended to other systems without a microwave drive.
