We study plasma wave excitation by an incoherent combination of a large number of low energy laser pulses (i.e., without constraining the pulse phases). We show that, in spite of the incoherent nature of electromagnetic fields within the volume occupied by the pulses, the excited wakefield behind the driver is regular and its amplitude is equal to that obtained using a single, coherent pulse with the same energy. Incoherent combination of multiple laser pulses may enable a technologically simpler path to high-repetition rate, high-average power laser-plasma accelerators, and associated applications.