comment/ator spoke too soon, I think, in telling you no. First, under the federal Fair Credit Reporting Act (FCRA), an employer must do two things before it may obtain a consumer report (a term which covers both credit reports and third party employment background checks) on an employee or applicant:
1. It must provide a stand alone conspicious notice telling the employee/applicant that a consumer report will be obtained and providing the employee/applicant a summary of his/her rights under the FCRA.
2. It must get from the employee/applicant express written consent to obtain the report.
Did the college do both of those things? And if they did, how were the notice and consent worded? Did they discuss consumer reports (a broad term that would cover both the the credit report and background check) or did it just say background check? The details matter, because it needed to have provided disclosure and consent that would cover the credit check. If the college did not do that then it violated the FCRA and you may have a claim for damages as a result of it.
Apart from the FCRA issue, there is a remote chance that declining the offer based on the credit report would amount to illegal discrimination under federal law. What kind of position did you apply for and what race are you? If the position is one for which there would be no good reason for the employer to need a credit report and you are of a minority race then the employer may have an illegal race discrimination issue.
I had thought potentially of a detrimental reliance claim, but it appears that the Pennsylvania Supreme Court killed that argument in this kind of context, making it not available in that state:
More importantly, equitable estoppel has been affirmatively rejected by this Court as an exception to the at-will rule. In Paul v. Lankenau Hospital, 524 Pa. 90, 569 A.2d 346 (1990), we held that “[t]he doctrine of equitable estoppel is not an exception to the employment at will doctrine. An employee may be discharged with o[r] without cause, and our law does not prohibit firing an employee for relying on an employer's promise.” Id. at 95, 569 A.2d at 348. Thus, the issue of whether Appellee detrimentally relied on any promises of the Authority is simply not relevant in determining whether Appellee has a protectable property interest in his employment.
Stumpp v. Stroudsburg Mun. Auth., 540 Pa. 391, 397, 658 A.2d 333, 336 (1995). Even in states where that claim might be a possibility the issue of damages is a problem because in most employment there is never any guarantee of how long the employment will last. You could be hired on and then fired after the first day of work, for example.
Many lawyers that litigate wrongful discharge/illegal discrimination cases will give you free initial consultations. You lose nothing but a little of your time to see an attorney, go over the details of this, and see if you might have something to pursue.