A worm algorithm is proposed for the two-dimensional spin glasses. The method is based on a low-temperature expansion of the partition function. The low-temperature configurations of the spin glass on square lattice can be viewed as strings connecting pairs of frustrated plaquettes. The worm algorithm directly manipulates these strings. It is shown that the worm algorithm is efficient, particularly if free boundary conditions are used. We obtain accurate low-temperature specific heat data consistent with a form c approximately T-2 exp [-2J/( kB T) ] , where T is temperature and J is coupling constant, for the two-dimensional +/- J spin glass.