It can't be done using an Action, but a lambda expression can also be treated as an Expression<Action> and then it becomes possible.
Note that the code below only works for this kind of expression: it uses the knowledge that we have a method call and that we use constants as parameters.
public class Program
{
    public static void Main(string[] args)
    {
        var values = GetParams(() => Test(1, 2));
        foreach (var v in values)
            System.Diagnostics.Debug.Print(v.ToString());
    }
    private object[] GetParams<T>(Expression<Func<T>> expr)
    {
        var body = (MethodCallExpression)expr.Body;
        var args = body.Arguments;
        return args.Select(p => ((ConstantExpression)p).Value).ToArray();
    }
    public int Test(int arg1, int arg2)
    {
        return arg1 + arg2;
    }
}