Yes, you can. You do not need to sign up for the Best Buy credit card to join their My Best Buy Loyalty program. In many ways the loyalty program is more beneficial than their credit card because not only does it allow you to earn points which can be redeemed for reward certificates (250 points earns a $5 reward certificate), but it also provides options for free shipping.
The rewards are identical to the base earned on their credit card. There is no credit check for loyalty program membership, anyone can apply and no one is denied. There are three tiers to the rewards program. The primary level is My Best Buy and then there are the elite and elite plus levels. To achieve elite status you must spend $1,500 per calendar year and your point bonus will increase by 10%.To achieve elite plus status $3,500 must be spent in a year. The salespeople will push their credit card and tell you that it will increase your rewards. This is true, however, the benefit of the half point extra is not significant enough to offset the high APR of the Best Buy credit card. Using almost any rewards credit card in conjunction with the Best Buy loyalty program will increase your rewards.