In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quantum wire with time-dependent random potential. Specifically, we study the electronic densities of states of a single and chains of quantum dots connected to two noisy leads.