This paper proposes a preliminary hypothesis of Quantum Fractal Time (QFT) and explores its possible mathematical structure and implications. The central hypothesis is that the structure of time may possess a local fractal character described by a scalar field α(x) with values in the interval (0,1]. The model introduces a dynamical field representing the local fractal dimension of time and explores its consequences in weak gravitational fields. The theory predicts small Yukawa-type corrections to gravitational time dilation, orbital dynamics, and perihelion precession. These predictions allow QFT to be constrained through comparison with precision tests of General Relativity.