This is the part of the Home Office Immigration Rules that applies to parents. I don't have any experience with this myself bit it looks like your mother would have to be financially dependent on you and have no close family in the US to qualify.
Requirements for indefinite leave to enter or remain in the United Kingdom as the parent, grandparent or other dependent relative of a person present and settled in the United Kingdom
317. The requirements to be met by a person seeking indefinite leave to enter or remain in the United Kingdom as the parent, grandparent or other dependent relative of a person present and settled in the United Kingdom are that the person:
(i) is related to a person present and settled in the United Kingdom in one of the following ways:
(a) mother or grandmother who is a widow aged 65 years or over; or
(b) father or grandfather who is a widower aged 65 years or over; or
(c) parents or grandparents travelling together of whom at least one is aged 65 or over; or
(d) a parent or grandparent aged 65 or over who has remarried but cannot look to the spouse or children of the second marriage for financial support; and where the person settled in the United Kingdom is able and willing to maintain the parent or grandparent and any spouse or child of the second marriage who would be admissible as a dependant; or
(e) parent or grandparent under the age of 65 if living alone outside the United Kingdom in the most exceptional compassionate circumstances and mainly dependent financially on relatives settled in the United Kingdom; or
(f) the son, daughter, sister, brother, uncle or aunt over the age of 18 if living alone outside the United Kingdom in the most exceptional compassionate circumstances and mainly dependent financially on relatives settled in the United Kingdom; and
(ii) is joining or accompanying a person who is present and settled in the United Kingdom or who is on the same occasion being admitted for settlement; and
(iii) is financially wholly or mainly dependent on the relative present and settled in the United Kingdom; and
(iv) can, and will, be accommodated adequately, together with any dependants, without recourse to public funds, in accommodation which the sponsor owns or occupies exclusively; and
(iva) can, and will, be maintained adequately, together with any dependants, without recourse to public funds; and
(v) has no other close relatives in his own country to whom he could turn for financial support; and
(vi) if seeking leave to enter, holds a valid United Kingdom entry clearance for entry in this capacity.