There is already a proposed constitutional amendment in the works to do just that, among various other measures at the state level, and it is ready for ratification in twenty-five of the thirty-eight states necessary to pass. Here's the text of the proposed amendment:

Section 1. We the People have compelling sovereign interests in the freedom of speech, representative self-government, federalism, the integrity of the electoral process, and the political equality of natural persons.

Section 2. Nothing in this Constitution shall be construed to forbid Congress or the States, within their respective jurisdictions, from reasonably regulating and limiting contributions and spending in campaigns, elections, or ballot measures.

Section 3. Congress and the States shall have the power to implement and enforce this article by appropriate legislation and may distinguish between natural persons and artificial entities, including by prohibiting artificial entities from raising and spending money in campaigns, elections, or ballot measures.

EDITED to correct; see the website for further details