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No, the Shop Your Way program is not a credit card nor does it offer financing. Sears does have a branded credit card that offers financing. However, the interest rate is very high. Also, if the balance you financed is not totally paid off within the time frame stated in the terms of the agreement then you will be charged the sky-high interest rate back from the original date of purchase.
There are many bank cards that offer 0% promotional interest periods. If your credit is good, which it would need to be in order to obtain the Sears card, you will be looking at a much lower interest rate on the 0% card after the promotional period has expired, compared to the Sears card which has a variable rate which hovers around 25%. Also you will not be charged the back APR in the event that you cannot pay your balance on time.