Probably not. As far as we can tell, to be a self-aware entity requires that we have a working brain, since we are what the brain does. Brain shuts down, we’re gone. So any hypothetical spirit entity that would be reincarnated independent of the brain hardware wouldn’t be “you” unless the brain-stored memories could be accessed too. Advocates of reincarnation are not usually too keen on grounding their views on the observable mechanics of neuroscience, however.
It is interesting, though, that anecdotal evidence for reincarnation tends to be in cultures that believes in reincarnation, just as it tends to be Roman Catholics who perceive images of the Virgin Mary in window stains or toast. Our human experiences are sufficiently broad and coincidence laden (think how many accidentally premonitory dreams must occur now and then out of the tens of billions of dreams that occur nightly on earth) that it shouldn’t come as a surprise that there is grist enough to be fitted into all manner of philosophical systems.
Implicit in the question would be the issue of who (or what) would one be reincarnated as? Do ants get to be reincarnated as people as often as the other way around? The notion of Karma (where ending up “higher” or “lower” depends on what you did before) is of course as laden with unverified presuppositions as trying to work out whether you get to keep your cat in heaven in a Christian context.
Given the speculative nature of the topic, then, I’ll suffice with that “probably not”. Or maybe add just that one shouldn’t depend on being reincarnated as a guide to behavior in this life. That maybe you should act as if this is literally your only chance, so that what good or ill you do won’t be made amends for by anything after you’re gone.
Live your life as you would want it to be remembered, for afterward only those remembrances by others are what are left to be known.
I can't claim to know whether every Memorial Day or Veterans Day observance excludes non-believers from the official observance when religious invocations are done, but it is fair to say we aren't taken note of generally.