  We study probability density functions (pdfs) of the circulation of velocity
and magnetic fields in magnetohydrodynamics, computed for a circular contour
within inertial range scales. The analysis is based on the instanton method as
adapted to the Martin-Siggia-Rose field theory formalism. While in the viscous
limit the expected gaussian behaviour of fluctuations is indeed verified, the
case of vanishing viscosity is not suitable of a direct saddle-point treatment.
To study the latter limit, we take into account fluctuations around
quasi-static background fields, which allows us to derive a sum rule relating
pdfs of the circulation observables and the rate of the strain tensor. A simple
inspection of the sum rule definition leads straightforwardly to the algebraic
decay $\rho(\Gamma) \sim 1/ \Gamma^2$ at the circulation pdf tails.
