A system is identifiable if and only if the relationship between the parameters and the input-output behaviour of the system is unique. If a system is not identifiable, then accurate parameter estimation is not possible because identical input-output behaviour can be obtained for several values of the parameters. Most identifiability work in the literature has focused on ordinary differential equation (ODE) models. In this work we propose a method for testing linear time-invariant (LTI) differential-algebraic (DAE) systems for identifiability. Our method is computationally efficient, allows the treatment of systems that are nonlinear in the parameters, and allows the construction of an identifiable realization of the system.