No, you can't... at least for now. The Google Play store and Apple Store have two different realms - apps downloaded in one realm do not carry ownership over onto the other realm. So, if the purchase of an app is made and tied to your Google Play ID, then that won't carry over to your Apple ID.
However, there are apps who require the user the create an account. Purchases made within that app with an app-specific account can get carried over. For example, if I buy filters for Aviary for Android and then move over to iPhone, those in-app purchases will be carried over as long as I use the same Aviary account for both "realms".