We present Security Relaxed Separation Logic (SecRSL), a separation logic for proving information-flow security of C11 programs in the Release-Acquire fragment with relaxed accesses. SecRSL is the first security logic that (1) supports weak-memory reasoning about programs in a high-level language; (2) inherits separation logics virtues of compositional, local reasoning about (3) expressive security policies like value-dependent classification. SecRSL is also, to our knowledge, the first security logic developed over an axiomatic memory model. Thus we also present the first definitions of information-flow security for an axiomatic weak memory model, against which we prove SecRSL sound. SecRSL ensures that programs satisfy a constant-time security guarantee, while being free of undefined behaviour. We apply SecRSL to implement and verify the functional correctness and constant-time security of a range of concurrency primitives, including a spinlock module, a mixed-sensitivity mutex, and multiple synchronous channel implementations. Empirical performance evaluations of the latter demonstrate SecRSLs power to support the development of secure and performant concurrent C programs.