Sponsoring a parent to live in the USA

Hi - I would really appreciate some advice on how to bring my mother to live with us in the United States.  We are Green Card holders currently living and working in Austin, Texas.  My mother is 73 years old and would like to move to the US from the UK to live with us.  She is past working age and will not be a "public burden" in  terms of being a liability on the US Government.  I am her only child.  Are there special circumstances or a dispensation that US Immigration will allow to enable us to sponsor her to live here?  Or do we have to wait to become US Citizens to apply for this?  Thanks