How to accredit my Ph.D. in USA
In the U.S., most academic fields are not like medicine: there is no licensing and for most purposes there are not strict legal requirements for what constitutes a degree.  In particular, there is nothing that needs to or can be done to accredit a foreign Ph.D.  (Other countries may differ.  For example, Germany used to treat non-EU Ph.D.'s differently; see http://www.zeit.de/2008/12/C-Seitenhieb-12.)

Regarding more specific issues:

Employers sometimes verify CVs, but that is not your responsibility.  If they need to check that you have a legitimate Ph.D. from Cairo University, then they will get in touch with the university directly to verify this.  You do not need to help (and in fact they won't allow you to help, to make sure the verification is unbiased), so all you need to do is to make sure everything on your CV is true.

You may run into people who acknowledge that you have a legitimate Ph.D. but have no idea what the standards of Cairo University are.  That will give you a modest disadvantage compared with students from, say, Stanford, but there's nothing you can do about it.  Ultimately, if you publish strong papers in prestigious venues, then that will matter much more than where your Ph.D. is from.  If you don't, then you will not get a research job anyway, wherever you studied.

If you are talking about upgrading the degree somehow - perhaps getting additional certification or even another degree from a particularly prestigious school - then it basically can't be done.  It's not truly impossible, and I know of a couple of cases in which people with Ph.D.s from other countries enrolled as students in the U.S. in order to improve their job chances.  However, most U.S. universities strongly discourage this, on the grounds that it's a waste of time and resources to devote a space in a graduate program to someone who already has a Ph.D. in the same field (or a closely related one).