Praise be to Allah.
It is better not to do that, because there is no evidence (daleel) for that. But it is prescribed for you to give in charity on behalf of your beloved relatives and others, if they were Muslims, and to make du’aa’ for them, and to perform Hajj and ‘Umrah on their behalf. But doing salaah and performing Tawaaf for them, and reading Qur’aan for them – it is better not to do these things, because there is no evidence for that.
Some scholars regard that as being permissible, by analogy with charity and du’aa’. But to be on the safe side you should not do it.
And Allaah is the Source of strength.