  We calculate the contribution of cosmic strings arising from a phase
transition in the early universe, or cosmic superstrings arising from brane
inflation, to the cosmic 21 cm power spectrum at redshifts z > 30. Future
experiments can exploit this effect to constrain the cosmic string tension Gu
and probe virtually the entire brane inflation model space allowed by current
observations. Although current experiments with a collecting area of ~ 1 km^2
will not provide any useful constraints, future experiments with a collecting
area of 10^4-10^6 km^2 covering the cleanest 10% of the sky can in principle
constrain cosmic strings with tension Gu > 10^(-10) to 10^(-12)
(superstring/phase transition mass scale >10^13 GeV).
