The closest verified source is a 1913 article in Indian Opinion: 'If we could change ourselves, the tendencies in the world would also change... We need not wait to see what others do.' The exact 'be the change' wording appears nowhere in the Collected Works of Mahatma Gandhi. The New York Times traced the compressed version in 2011 (Brian Morton, 'Falser Words Were Never Spoken'), finding it only in later secondary retellings.
The short form spread through 1980s and 90s activist merchandise, posters, and email signatures, then hardened into 'Gandhi said' through sheer repetition. It survives because it is better branding than the original paragraph.
The 1913 passage is almost the opposite of a call to personal power: change yourself, it says, and the world's tendencies shift as a side effect, without waiting for anyone else. The fake version commands; the real one reduces your jurisdiction to one person.
If the real passage is about how small one person's sphere of control is, why does the fake version flatter you?