There is nothing to stop anyone from applying for a mortgage. Getting approved—that is a different matter. I will assume you meant the latter.
Purchasing a home with less than perfect credit score
“Poor” is subjective. If you mean, “not perfect,” I would say you may be okay to get approved. Contrary to what the common narrative claims, mortgage qualifying standards are NOT “insanely high.”
Certain items show up in credit reports that have to be resolved before getting approved for a mortgage. Among these are tax liens, collection accounts, and unsatisfied judgments. Resolving those items will also raise credit scores—sometimes very significantly.
There are other, non-derogatory items that can lower your credit score. Heading the list is credit card utilization. Once your balance on any revolving account (credit card) exceeds about 30% of the credit limit, your score will start to suffer. Paying your cards down is an excellent way to start healing your credit.
Remember this when purchasing a home with less than perfect credit
The first thing you should do when thinking about buying a home is to create a relationship with a loan officer you feel you can trust. This will probably be someone working for a “non-depository lender;” that means a mortgage banker, rather than a commercial bank. The loan officer will start by collecting documentation from you needed for loan approval—tax returns, pay stubs and bank statements. He or she will pull a credit report and let you know quickly if you qualify now, and for how much. If your score is too low to qualify, the loan officer should give you an action plan to raise your financial profile into the green.
The most important thing is to realize that you CAN do this. It may not happen overnight, but it is definitely in your future.