  Cosmic strings are topological defects which can be formed as a result of
phase transitions with a spontaneous symmetry breaking in the early Universe.
The possibility of the generation of a magnetic field around a cosmic string on
the Grand Unification energy scale (GUT scale) in the early Universe
immediately after the termination of the deconfinement-confinement phase
transition has been analyzed. It is found that a circular current and a
magnetic field directed along the string are induced around the string in the
vacuum of a pseudoscalar matter consisting of charged pions. We also have
studied the interaction between the magnetic flux tube surrounding the string
(the string magnetosphere) and the cosmic plasma in the early Universe. A
possibility of magnetization of the cosmic plasma surrounding the string owing
to its interaction with the string magnetic field has been analyzed.
