Future quantum computation and networks require scalable monolithic circuits, which incorporate various advanced functionalities on a single physical substrate. Although substantial progress for various applications has already been demonstrated on different platforms, the range of diversified manipulation of photonic states on demand on a single chip has remained limited, especially dynamic time management. Here, we demonstrate an electro-optic device, including photon pair generation, propagation, electro-optical path routing, as well as a voltage-controllable time delay of up to ~12 ps on a single Ti:LiNbO3 waveguide chip. As an example, we demonstrate Hong-Ou-Mandel interference with a visibility of more than 93 ± 1.8%. Our chip not only enables the deliberate manipulation of photonic states by rotating the polarization but also provides precise time control. Our experiment reveals that we have full flexible control over single-qubit operations by harnessing the complete potential of fast on-chip electro-optic modulation.