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In this paper, we examine the concept of twisted Rota-Baxter (TRB) operatorson associative conformal algebras. Our strategy begins by constructing an$L_\infty$-algebra using Maurer-Cartan elements derived from $H$-twistedRota-Baxter ($H$-TRB) operators on associative conformal algebras. Thisstructure leads us to explore the cohomology of the conformal $H$-TRB operator,which is characterized as the Hochschild cohomology of a specific associativeconformal algebra with coefficients in a conformal bimodule. Furthermore, westudy the linear and formal deformations of conformal $H$-TRB operators toexplore the application of cohomology.

Cohomology of Twisted Rota-Baxter operators on Associative~Conformal Algebra