The problem of estimating the parameters in a continuous-time ARX process from unevenly sampled data is studied. A solution where the differentiation operator is replaced by a difference operator is suggested. In the paper, results are given for how the difference operator should be chosen in order to obtain consistent parameter estimates. The proposed method is considerably faster than conventional methods, such as the maximum likelihood method. The Cramer-Rao bound for estimation of the parameters is computed. In the derivation, the Slepian-Bangs formula is used together with a state-space framework, resulting in a closed form expression for the Cramer-Rao bound. Numerical studies indicate that the Cramer-Rao bound is reached by the proposed method.