The short answer is: you can't.
The long answer is that since we're searching for a new definition of a term when removing a necessary (in my opinion) precondition for it to exist, the question becomes "can you make up a new definition for what you intuitively and empirically understand as intention, while removing free will from the picture?". I'm going to give it a shot.
First of all, there's a lot to be said about whether or not the idea or intuition of intention even exists in our collective discourse based on the latent assumption that free will is a thing. As in, before any rigorous definition, even the intuitions encoded in discourse, philosophy, art, and other languages as "intention" could very well be as invalid as the assumption of free will itself.
That being said, I'm a fan of Deleuze's model for people and other entities as machines of input, output and internal state (not his wording, but I paraphrase and in consequence, interpret and alter for the purposes of my point). It's not perfect, but I run to it a lot to answer these question as I find it very refreshing, often lacking in bias and having good explanatory power compared to the usual romance-foo that dominates these conversations. If that's the case you could pretty much define intention not as a self-started force but as a product of a much blurrier mechanism, namely the non-deterministic characteristic of this rhizomatic soup. Whether or not an input or output will exist, what kind will it be, what internal state will it find or cause in the machine and the long term dependencies between these interactions seem to me like a convincing enough candidate for the cause of any intuition (or illusion if you like a more cynic vocabulary) of "intention". It's pretty much an emergent symbol we use, assuming the form of a force for the setup and function of new connections, that will in their complication or pure non-determinism spawn even more intention in the network.
tl;dr: Intent could be the most basic expression of the RNG of the universe.