A tunable ultrafast intensity-rotating optical field is generated by overlapping a pair of 20 Hz, 800 nm chirped pulses with a Michelson interferometer (MI). Its rotating rate can be up to 10 trillion radians per second ($\text{Trad}/\text{s}$), which can be flexibly tuned with a mirror in the MI. Besides, its fold rotational symmetry structure is also changeable by controlling the difference from the topological charges of the pulse pair. Experimentally, we have successfully developed a two-petal lattice with a tunable rotating speed from $3.9~\text{Trad}/\text{s}$ up to $11.9~\text{Trad}/\text{s}$, which is confirmed by our single-shot ultrafast frame imager based on noncollinear optical-parametric amplification with its highest frame rate of 15 trillion frames per second (Tfps). This work is carried out at a low repetition rate. Therefore, it can be applied at relativistic, even ultrarelativistic, intensities, which usually operate in low repetition rate ultrashort and ultraintense laser systems. We believe that it may have application in laser-plasma-based accelerators, strong terahertz radiations and celestial phenomena.