We present a general method for calculating inclusive cross sections f
or the production of heavy quarkonium states with definite polarizatio
n within the NRQCD factorization approach. Cross sections for polarize
d production can involve additional matrix elements that do not contri
bute to cross sections for unpolarized production. They can also inclu
de interference terms between parton processes that produce Q (Q) over
bar pairs with different total angular momentum. The interference ter
ms cancel upon summing over polarizations. Our method can be generaliz
ed to N dimensions and Is, therefore, compatible with the use of dimen
sional regularization to calculate radiative corrections. We illustrat
e the method by applying it to the production of J/psi via the parton
processes q (q) over bar --> c (c) over bar and gg --> c (c) over bar.