Plants perceive highly variable environments and biotic interactions through membrane receptors like the GLutamate Receptor-like (GLR) family, related to the ionotropic Glutamate Receptors that underlie information transmission in neurons. GLRs underpin information transduction and morphological adaptations in plants. However, mechanistic understanding is scarce. In Arabidopsis thaliana roots, we investigated how GLRs underlie amino acid-induced electric and Ca2+ excitability. We also assessed the contribution of GLR3.7 in root hair elongation. We present GLRs as mediators of a local, glutamate-induced electric and Ca2+ response in roots, with the same initiation kinetics of wound-induced Slow Wave Potentials (SWP). We identify GLR3.7 as mediator of root hair elongation through maintenance of membrane depolarization at the growing cell apex. These results propose a parallel between glutamate-triggered signals and SWP initial phase as local and chemically induced, and posit GLR3.7 as a possible contributor to Ca2+ homeostasis in root hair apical growth.