Only locally licensed individuals, i.e. chartered accountants, shall become partners and hold equity share in accounting or auditing firm. A chartered accountant can practise Accounting and Auditing either individually or in partnership with chartered accountants or in partnership with members of such other recognised professions as may be prescribed by ICAI or Government. Foreign accountants can become locally licensed Chartered Accountant (CA) on reciprocity basis according to section 29 of the Act.
"4. Entry of names in the 4[Register of members].—(1) Any of the following persons shall be entitled to have his name entered in the 4[Register of members], namely,-[…]
[(v) any person who has passed such other examination and completed such other training [outside India] as is recognised by the Central Government or the Council as being equivalent to the examination and training prescribed for members of the Institute: Provided that in the case of any person who is not permanently residing in India, the Central Government or the Council, as the case may be, may impose such further conditions as it may deem fit;] 
[...]
CHAPTER IV - REGISTER OF MEMBERS
19. [Register of members].—[(1) The Council shall maintain a Register of members of the Institute in such manner as may be prescribed.]
(2) The [Register of members] shall include the following particulars about every member of the Institute, namely,— (a) his full name, date of birth domicile, residential and professional addresses; [no citizenship requirement]
[...]
CHAPTER VIII - MISCELLANEOUS
29. Reciprocity.—(1) Where any country, specified by the Central Government in this behalf by notification in the official Gazette, prevents persons of Indian domicile from becoming members of any institution similar to the Institute of Chartered Accountants of India or from practicing the profession of accountancy or subjects them to unfair discrimination in that country, no subject of any such country shall be entitled to become a member of the Institute or practice the profession of accountancy in India.
(2) Subject to the provisions of sub-section (1), the Council may prescribe the conditions, if any, subject to which foreign qualifications relating to accountancy shall be recognised for the purposes of entry in the 3[Register  of members]. [...]" (THE CHARTERED ACCOUNTANTS ACT, 1949, as amended)
THE CHARTERED ACCOUNTANTS ACT, 1949, as amended
[<a href="https://www.indiacode.nic.in/handle/123456789/1552?view_type=browse&sam_handle=123456789/1362">Act</a>]