We analyse the non-commutative U(1) sigma model, which arises from the vacu
um dynamics of the non-commutative charged tachyonic field. The sector of "
spherically symmetric" excitations of the model is equivalent to a chain of
rotators. Classical solutions for this model are found, which are static a
nd "spherically symmetric" in non-commutative spatial dimensions. The limit
of small noncommutativity reveals the presence of Polyakov vortices in the
model. A generalisation of the model to q-deformed space, which may serve
as a regularisation of the non-deformed model is also considered.