Electrons in solids are classified by several quantum numbers, including their momentum, spin, and sometimes the orbital angular momentum (OAM). In some cases two or more degrees of freedom appear in coupled form as, for instance, in the Rashba phenomena where there exists a one-to-one correspondence between the electron's momentum and its spin. Here we show that a similar correspondence between momentum and OAM must exist, on surface bands where the inversion symmetry is broken. Strong spin-orbit interaction (SOI) is not a requirement. As a method to detect such OAM-momentum correspondence, we propose the circular dichroism (CD) experiment using the angle-resolved photoemission (ARPES) setup and derive the relationship between the local OAM in momentum space and the CD signal.