I got my Macy's card (with a $100 limit) when I didn't have ANY credit score - although I know that doesn't really help answer as to what the minimum score they'd want would be, I do know that they will approve people who don't even have a credit score or any sort of credit file for them to check.
I know I didn't have a credit file, as I'd only moved to the US on the Saturday, and went into Macy's on the following Monday about 20 minutes after opening a checking account, to buy some kitchen stuff. Wouldn't have dreamed of trying to get a card, but the sales assistant seemed convinced I would get one. I didn't have a social security number at that point, even - she said that didn't matter!
This is just what I've heard, rather than 'fact', but I think applying instore when making a purchase has a higher chance of getting accepted than just applying online - you might get accepted for a very low limit at first, but Macy's are very good with credit line increases. You can ask them to increase your limit every 90 days - I didn't find that out until I'd had my card for 6 months, but have called every 3 months since then and now have a $1400 limit.