I was wrongfully accused of stealing Walmart property, Can i sue for wrongful accusation and defamation of character?

There is no case for defamation or "wrongful accusation" (never heard of that claim, but New Jersey might have one), based on the facts you stated. This was likely a good-faith mistake, given the management's apologetic efforts and offer of a gift card following the rectification of the issue, and even if you suspect that the accusation was in fact malicious, your post contains no facts from which that less than honorable motive can be inferred. I understand and sympathize with your frustration, however; most of us would have felt humiliation had we been in your shoes. I hope your angst over this will not be long-lasting. Have a good week.

As both my colleagues already stated there is no case here. This would have had to go much further such as a wrongful arrest and furthered by malicious prosecution unsupported by evidence. Also this probably shouldn't be posted under criminal defense. If you got arrested we could help ;) Sounds more like you're looking for a civil attorney.

Unfortunately, as my colleague referenced in the above response, there does not seem to be any damages. One of the essential elements of proving defamation is damages suffered by the plaintiff. Though you may have been embarrassed by the situation, without further information outside of what you provided, there does not seem to be any damages that you suffered, most specifically, to your reputation.