Unfortunately we cannot tell you as it depends where you live.
We have heard from members where it has taken a few weeks to over 6 months.
You can contact PIP just to check that they have received the forms, some claimants are receiving a text message informing that DWP has received their claims form others have not. If you sent it by recorded delivery, check on line when it was delivered and who signed for it and then contact DWP.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems