Even state verbs are sometimes used in the continuous, eg. "I'mmm loving it".
"have to" is a semi-modal/periphrastic modal with a meaning, as you almost certainnly know, similar to the modal verb 'must'.
While true modals do not use 'ing' forms, periphrastic modals sometimes do. Your example could be used by someone to show a more immediate situation, a more onerous situation, to denote that they really aren't happy about "having to study".
An exact phrase google search gave the following results.
Results 1 - 10 of about 382,000 English pages for "I'm having to".
Why not try an exact phrase search yourself, then you can look at some of the examples to see how it's used?