Exploiting the infinite-order continuous dynamical rotational symmetry of circularly or elliptically polarized classical light pulses, we establish the conservation law between the angular momentum and energy in strong-field ionization that is applicable at the subcycle level. We illustrate the conservation law through the correlated spectrum of angular momentum and energy of photoelectrons, both at the tunnel exit and in the asymptotic region. Moreover, we propose a protocol based on electron vortices to directly visualize the existence of the subcycle conservation law. Our work paves the pathway toward a deeper understanding of fundamental light–matter interactions on the subcycle scale.