In this paper, we analyze a singularly perturbed convection-diffusion delay problem with Robin condition. In order to solve this problem numerically, we construct a fitted difference scheme on a uniform mesh. The scheme is based on the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. We prove that the method is first order convergence in the discrete maximum norm. Also, we present numerical results that support the theoretical results.