The OED1 suggests that this was the original meaning of anthropomorphism, though I think the more general meaning (The OED's definition 1.b.) now clearly predominates.
a. The attribution of human form, character, or attributes to God or a god.
b. The attribution of human personality or characteristics to something non-human, as an animal, object, etc.
Luckily, the OED offers several more obscure options that probably retain their specifically theistic meaning:
anthropomorphite, n. and adj.
Of, relating to, or characterized by anthropomorphitism; spec. that ascribes human form, character, or attributes to God. Cf. ANTHROPOMORPHITIC adj.
The doctrine or beliefs of anthropomorphites; (more generally) anthropomorphism; the ascription of human form, character, or attributes to God. Cf. anthropomorphism n. 1a, anthropomorphite n.
The action or an act of conceiving of or regarding God or a god as having human form or characteristics; the fact or process of becoming anthropomorphized; (more generally, with reference to objects, animals, etc.) anthropomorphism.
1. Characterized by or involving the attribution of human feelings and emotions to God or a god; = ANTHROPOPATHIC adj.
Characterized by or involving the attribution of human feelings and emotions to something other than a human being, esp. to God; displaying anthropopathy.
1. Theol. The doctrine of the union of the divine and human natures, or of the manifestation of God as man, in Christ.
2. Mythol. The attribution of human nature or character to the gods.
theˈanthropist n. a believer in theanthropism (also attrib. or as adj. ).
Also anthropomorphitic, anthropomorphitical, anthropophuistic, and anthropopsychic, though all of those are very rare and the last may include the more general meaning of anthropomorphic.
I don't see much to distinguish these one from another, so I think you could pick the one you like the sound of. "Theanthropism" and "theanthropist" may have the most transparent meaning.
1 All definitions are from OED Online, Oxford University Press. Unfortunately, this is a subscription, paywalled service; if you do not have access, check with your local or school library, as many of these have subscriptions which patrons can access. Note that all of the "anthropo-" entries have been updated to the OED 3rd Edition, March 2016, but "theanthropism" has not yet been revised.