No Delta will not pay for your rental car due to a changed arrival time.

You can look to see if there is another Delta itinerary that would work better and, depending on the amount the arrival time changed, they may be willing to change you to a new flight, but you would need to call and ask. Before you call, look up your flight options. You may also be able to ask for a refund and book on another airline. Again all of this depends on the length of the change. If it's only 15 minutes, unlikely, but there is no harm in asking them to change your flights (the worst they can say is no). Greater than an hour, more likely.