A BDDC preconditioner is defined by a coarse component, expressed in terms of primal constraints and a weighted average across the interface between the subdomains, and local components given in terms of Schur complements of local subdomain problems. A BDDC method for vector field problems discretized with Raviart-Thomas finite elements is introduced. Our method is based on a new type of weighted average developed to deal with more than one variable coefficient. A bound on the condition number of the preconditioned linear system is also provided which is independent of the values and jumps of the coefficients across the interface and has a polylogarithmic condition number bound in terms of the number of degrees of freedom of the individual subdomains. Numerical experiments for two and three dimensional problems are also presented, which support the theory and show the effectiveness of our algorithm even for certain problems not covered by our theory.