The first problem is that you cannot tell what free will is without giving a definition, but it is hard to give an appropriate operational definition without already implicitly answering your question, viz. taking a stance.

The second problem is that randomness can be characterized in many different ways and these definitions are not fully equivalent. Unpredictability is an important criterion in cryptography, but does not work as a general criterion for itself, for it is too unclear. For example, if you record a sequence of random numbers (generated from radioactive decay) for later use, you may "predict" them before they are used, because you have already recorded them, yet they would still be random numbers. Vice versa, many deterministic processes can be unpredictable in practise. A slightly better practical definition of randomness is that a sequence of numbers is random if you cannot compress it and it satisfies some additional statistical criteria. (That practical measure is related to Kolmogorov complexity.) The problem is that a sequence of numbers might pass all these tests and still not be random, i.e. you cannot really tell from a sequence whether it is random or not by looking at the numbers alone. A random generator outputting characters may spit out all works of Shakespeare at any time, although this is highly unlikely.

Third, non-determinism involves a random choice between alternatives.

So what does this have to do with free will? Since a random choice would not be a choice of <i>your</i> free will but rather a choice made by the respective random source, a choice made of free will does not seem to be the same as a non-deterministic choice. Since on the other hand we do not consider a deterministic choice to be a choice of free will either - perhaps not even a choice at all - the concept of free will might be inconsistent after all. In any case, without a proper definition of free will we cannot give an answer to your question, and if you had this definition you would likely have answered the question already for yourself.

There are two easy ways out of this dilemma: (1) Discard free will in the sense of accepting determinism. (2) Discard free will in the sense of accepting that free will  consists of highly complex, non-deterministic, yet rule-based choices.

I personally opt for (2), because it is more in line with modern physics than (1) and supported by the view that human brains are <i>open</i> information processing systems. (Notice that a computational system with the ability of making non-deterministic choices is not a Turing machine, although it might be an extension of one.)