In David Rankine and Sorita D'Este's excellent book The Isles of Many Gods, the Cerne Abbas Giant is amongst those listed (p157). This is 'an A-Z of the Pagan Gods and Goddesses worshiped in Ancient Britain during the First Millennium CE through to the Middle Ages'.
For them, and for everyone protesting the Homer Simpson incident from a Pagan viewpoint, the figure on the hillside is Helis, aka Helith.
Their cited source is HJM Green's archaeological research for Oxford University, which was published in Pagan Gods and Shrines of the Roman Empire (1984).
He concluded that there was undoubtedly a God local to Cerne Abbas called Helis. He also observed that people in the local towns and villages still referred to the chalk figure as Helis.
Green then speculated that Roman invaders had imported their God Hercules into the British Isles. The native Celts had then Cymrized the name into Helis and that was who was etched into the chalk.
This theory was given a further boost in 1997, when a geological survey revealed that the Cerne Abbas Giant has changed over the years. He used to have a cloak draped over his arm too, as well as a severed head at his feet. As you can see in the image of Hercules above, the knotted club and cloak are certainly associated with him.
(Incidentally, Cerne Abbas Giant didn't used to have such a large phallus either. He had a distinct circle as a naval, which eventually became merged with his previously smaller erection.)
Unfortunately, all of this is largely circumstantial evidence, based too strongly on oral history. There is nothing wrong with the latter, until you realize that Helis or Helith has a better etymology in Saxon lore and they never met the Romans in Britain.
In the 16th century, John Leland visited St Augustine's Well, in nearby Cerne Abbey. He found that the spring was known for its restorative properties; and that it had originally been dedicated to Helith, a Saxon God or Goddess. The name comes from the same root as the word 'health'.
After the Norman conquest, Gotselin the Frenchman became Archdeacon of Canterbury. He used the position to study the life of St Augustine. In 1099, Gotselin completed his Historia Translationis St Augustini, which discussed the saint's evangelism in the Cerne Valley.
The locals worshiped Hegle or Heil. Statues of the God (or Goddess) lined the well. But Augustine smashed them all before converting the 'Heathens' into Christianity. The spring was renamed there and then as St Augustine's Well. Gotselin cited an unnamed Saxon source, which dated that as occurring around 603 CE.
All of this very firmly places Helis (or a variation of the name) in the area right at the foot of Giant's Hill. We can be certain that the deity was worshiped in the Cerne Valley before the coming of Christianity.
What none of it does is point categorically to the chalk figure upon the hill and state, "That is Helis."
The deity in question was apparently associated with water and, in Britain, those tend to be Goddesses. The person outlined on the hill is very, very obviously masculine.