Embedding a magnetic electroactive molecule in a three-terminal junction allows for the fast and local electric field control of magnetic properties desirable in spintronic devices and quantum gates. Here, we provide an example of this control through the reversible and stable charging of a single all-organic neutral diradical molecule. By means of inelastic electron tunnel spectroscopy we show that the added electron occupies a molecular orbital distinct from those containing the two radical electrons, forming a spin system with three antiferromagnetically coupled spins. Changing the redox state of the molecule therefore switches on and off a parallel exchange path between the two radical spins through the added electron. This electrically controlled gating of the intramolecular magnetic interactions constitutes an essential ingredient of a single-molecule quantum gate.