Yes you can apply for a PAN card
Income Tax Department allots PAN Card to minors without hassles
PAN Card is mandatory required in case you intent to make them a nominee on your investments like property, stocks and any other financial product. So in case you intent to make your minor child, a nominee for your investments, you would be required to furnish the PAN Card of the Minor Child
The procedure for applying for the PAN Card for Minors is fairly simple. The parents of the minor would be required to submit an application in Form 49A. This form can be submitted online as well as offline.
Documents for Proof of Identity, Proof of Address and Proof of Date of Birth are required to be submitted while making the application. The Birth Certificate of the minor would be a valid proof for the Date of Birth.
In case of minors, the proof of identity and proof of address of either parent would be required to be submitted. The application should also be signed by the parent whose documents have been submitted. The signature of the parent would be printed on the PAN Card