Can I, personally? No. Somebody who does genetic engineering for a living would have a far better chance of proposing such a test, were one to exist, as he'd have some idea of what to look for.
Now, given that I readily acknowledge that random mutation plays a role in biological phenomena, I am not bothered by the possibility that random mutation could be responsible for sickle-cell traits. (And, given that sickle-cell traits confer some degree of immunity to malaria, I can see a mechanism by which this trait would be passed on naturally.) So a lack of a suitable corresponding test for "alien induced sickle-cell traits" would be no big deal to me.
Then again, we know that humans can at least pursue similar results -- for example, a great deal of progress is being made in the field of gene therapy for cystic fibrosis.
The question in that case would be: could one think of a test to determine whether the results of the cystic fibrosis gene therapy came as a result of random mutation? At the same time, could one think of a corresponding test to determine whether the gene resulted from intelligent agents?