There are several IRT packages for R (https://cran.r-project.org/web/views/Psychometrics.html), which is inexpensive (FREE) but many people find it less easy to use than SPSS (I used to use both in teaching). STATA has a new set of procedures for IRT and it is comparable to SPSS regards ease of use (and many find it easier). It looks good.  SAS, Systat, and many others also allow this, and your university should have licenses for these. There are specialist IRT packages available http://www.ssicentral.com/irt/.  I used these specialist packages for the attached paper, but now mostly use R. It depends on what type of IRT you wished to do.

Article A dialogue about MCQs, reliability, and item response modelling

I should add that a lot of the IRT models can be run with software not specifically designed for those models, like multilevel software (that allows binary responses) and Bayesian software. See for example https://github.com/stan-dev/example-models/tree/master/misc/irt for doing this with the Bayesian software STAN. I am adding this more for completeness than a recommendation since this software is less user-friendly than the point-and-click menu-driven interfaces of STATA, SYSTAT, etc. But, if you have some complex model adapting these is an alternative.

You may want something simple and straightforward and standalone

The Berkeley Evaluation and Assessment Research Center has this software

http://bearcenter.berkeley.edu/software/constructmap

at the other end of the scale is

De Boeck, P. & Wilson, M. (Eds.). (2004). Explanatory item response models: A generalized linear and nonlinear approach. New York: Springer-Verlag.

Chapter 12 considers software and how to use the multilevel software that Daniel refers to

https://books.google.co.uk/books/about/Explanatory_Item_Response_Models.html?id=pDeLy5L14mAC&source=kp_cover&redir_esc=y

For R, this Task view covers a lot of possibilities

https://cran.r-project.org/web/views/Psychometrics.html

Stata 14. Very simple (for the IRT). Great manuals.