Energy can be defined in physics as the ability to perform work, as you say, and measured in joules or equivalent units. You ask whether we can ascribe energy to God in this sense. The ability of God to act in the world is a different question - I think you are asking about being able to measure God's own energy in some sense, whether this is kinetic energy or potential energy or anything else.
To calculate such a quantity, we would need to take measurements of some kind and somehow end up with a value in units of kg.m2.s-2 = J. This effort is stymied since there is no way to measure God's mass, length, etc., as these kind of measurements cannot apply to God. That is, we cannot measure God's energy for the same reason that we cannot measure his size - there is nothing special about energy in this regard. Can we measure his kinetic energy (= energy that depends on mass and velocity)? No, because God has neither. Potential energy (= energy that depends on position within a gravitational field)? No, because God is not located in a gravitational field, and indeed is not located at any point in space. Moreover, there is no particular reason to believe that even if he had energy, he would be subject to conservation of energy (we're not going to get very far trying to apply Noether's theorem).
This goes beyond a mere practical difficulty (I mean, it is not true to say that God has mass but we just can't calculate it). Theologically, attributes like "mass" cannot be applied to God, because God is an altogether different kind of thing than ordinary people or objects. The argument goes something like this. God's existence is pure (in scholastic terminology, he is actus purus, pure action) because his existence is (1) not dependent on anything else, (2) unchanging, and (3) he has no potential to be different from what he is. Hence it is a category error to apply any contingent attribute to God - any quality or quantity that we could imagine varying over time or in different circumstances. Mass is this kind of quantity. See Aquinas, Summa Theologica, Part 1 Q3 for the classic exposition. He talks about height, depth, colour and temperature being inapplicable concepts but it's the same idea.
Admittedly, some people have tried to apply concepts like "energy" to God. Teilhard de Chardin continually used the language of physics, in a dubious way, and in particular talked about humans having "spiritual energy" which would increase and merge with God's spiritual energy. But:
...he uses in metaphor words like energy, tension, force, impetus and dimension as if they retained the weight and thrust of their specific scientific usages. Consciousness, for example, is a matter upon which Teilhard has been said to have illuminating views. For the most part consciousness is treated as a manifestation of energy, though this does not help us very much because the word 'energy' is itself debauched; but elsewhere we learn that consciousness is a dimension, or is something with mass, or is something corpuscular and particulate which can exist in various degrees of concentration, being sometimes infinitely diffuse.
That's from the famous critical review by Peter Medawar of The Phenomenon of Man. It is a great reminder to be very careful about overinterpreting or misapplying concepts from physics.
