Assume given an algebraic stack(*) $\mathcal{X}$ with presentation $X_0 \to \mathcal{X}$, and the corresponding groupoid $X = (X_0\times_\mathcal{X} X_0 \rightrightarrows X_0)$ in algebraic spaces (or schemes, given the right sort of algebraic stack(*)).

(*)Allow me to be a little loose with the definition. Take your favourite sort of alg. stack if you like.

Who first proved that $\mathcal{X}$ is equivalent to the stack of $X$-torsors?

I'm interested not just for a reference, but in the technique, at least from a category-theoretic point of view.