Answer set programming (ASP) is a declarative programming paradigm for solving search problems arising in knowledge-intensive domains. One viable way to implement the computation of answer sets corresponding to problem solutions is to recast a logic program as a Boolean satisfiability (SAT) problem and to use existing SAT solver technology for the actual search. Such mappings can be obtained by augmenting Clark's completion with constraints guaranteeing the strong justifiability of answer sets. To this end, we consider an extension of SAT by graphs subject to an acyclicity constraint, called SAT modulo acyclicity. We devise a linear embedding of logic programs and study the performance of answer set computation with SAT modulo acyclicity solvers.