The theory of relativistic plasmas is attracting interest as a model of high-energy astronomical objects. The topological constraints, built in the governing equations, play an essential role in characterizing the structures of plasmas. Among various invariants of ideal models, the circulation is one of the most fundamental quantities, being included in other invariants like the helicity. The conventional enstrophy, known to be constant in a two-dimensional flow, can be generalized, by invoking Clebsch variables, to the topological charge of a three-dimensional fluid element, which essentially measures circulations. Since the relativistic effect imparts space-time coupling into the metric, such invariants must be modified. The non-relativistic generalized enstrophy is no longer conserved in a relativistic plasma, implying that the conservation of circulation is violated. In this work, we extend the generalized enstrophy to a Lorentz covariant form. We formulate the Clebsch representation in relativity using the principle of least action and derive a relativistically modified generalized enstrophy that is conserved in the relativistic model.