  We use lattice Monte Carlo simulations to study non-perturbatively the
tension, i.e. the free energy per unit length, of an infinitely long vortex in
the three-dimensional U(1)+Higgs theory. This theory is the low-energy
effective theory of high-temperature scalar electrodynamics, the standard
framework for cosmic string studies. The vortex tension is measured as a
function of the mass parameter at a large value of the Higgs self-coupling,
where the transition between the phases is continuous. It is shown that the
tension gives an order parameter that can distinguish between the two phases of
the system. We argue that the vortex tension can describe the physics of long
strings without lattice artifacts, unlike vortex network percolation.
