Carrier-envelope-phase (CEP) of sub-cycle ultraviolet (UV) pulse strongly influences the dynamics of quantum systems, but its characterization is not accessible experimentally. Here we investigate photodissociation of a diatomic molecule from its ground-rovibrational state in a linearly polarized weak sub-cycle UV pulse with a controlled CEP. The angular distribution of photofragments shows an asymmetric profile deviating from the well-known cos(2-) or sin(2)-like ones, which can be identified as a way to imprint CEP. We unveil that such an effect stems from the temporal neighboring rotational excitation by molecular permanent dipole interaction through the joint contributions between counter-rotating and rotating terms. This in turn, opens different pathways in photodissociation dynamics. Given that the temporal excitation between various states with close energies can be manipulated by CEP of subcycle UV pulses, our results pave ways for understanding and manipulating electron, nuclear and their joint dynamics with variation of CEP of attosecond pulses.