Don't open a margin account at a brokerage and you will not be subject to a credit check. The only information that a brokerage will look for when you open a regular account with them is whether you have a valid bank account and Social Security number. If you do apply for a margin account, the brokerage will run a credit check on you, but in most cases you will be approved even if you have a terrible credit rating.
Ensure that you have a valid bank account before you attempt to open a brokerage account. As long as you provide accurate banking and personal identification information to your brokerage, you aren't likely to have any issues opening an account.
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Deposit money into your brokerage account from your bank account. Pay all relevant fees when doing so. The brokerage firm will check your status with ChexSystems, but it won't run a credit check on your file.
Invest in stocks using the funds in your brokerage account. Your brokerage will not deny you the use of your stocks due to a bad credit rating. If a judgment is obtained against you due to debts, however, your creditors may be able to seize or garnish portions of your brokerage account.
Consider attempting to open a margin account even if you have a bad credit rating. If you want to trade on margin, the brokerage firm generally cares only whether you have available funds to pay it back if you receive a margin call. The brokerage will check your credit rating, but it's mostly just a formality. Students are not allowed to open margin accounts.