In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is quantum electrodynamics – the theory of electrons interacting with the electromagnetic field – based on $U(1)$ gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. While quantum computers suggest a way forward, it is difficult to build large-scale digital quantum devices required for complex simulations. Here, we propose a fully scalable analog quantum simulator of a $U(1)$ gauge theory in one spatial dimension. To engineer the local gauge symmetry, we employ inter-species spin-changing collisions in an atomic mixture. We demonstrate the experimental realization of the elementary building block as a key step towards a platform for large-scale quantum simulations of continuous gauge theories.