Yes, the Instacart Mastercard does a hard inquiry on your credit report when you apply. A hard inquiry usually results in a slight decrease in an applicant's credit score, but the effect only lasts for a short period of time. The hard inquiry allows Chase to determine your credit risk and ultimately decide whether you'll be approved for an account.
The Instacart Credit Card requires good credit to be approved. You can check your credit score by signing up for a free WalletHub account. You'll have access to free credit scores and free credit reports, both updated daily.