You need the OR standard error to do that. Z-scores and p-values only describe your confidence that your estimated odds ratio isn't actually coming from the null. Your p-value is roughly a function of your power to detect a SNP and the effect of that SNP.
If all I know is that I have a p-value of 1e-9, then it's possible that this p-value came from a SNP with a big effect in a small cohort (low power and high effect), or a large effect SNP in a large cohort (high power and low effect). I can't distinguish these two without more information.