They are more closely linked than one might think. Here's how I see it:

Poetry calls upon the power of metaphor and feeling while prayer calls upon the power of God and Holy Spirit. Poetry uses metaphor and imagination to transform and elevate feeling and perception.

Prayer resets one’s innermost longings and aspirations to be more closely aligned to the will of God. With both there is a giving over to a higher power. There is a surrender of personal ego and will to the Holy Spirit or to the creative muse within.

Prayer and Poetry Transcend Ego-Mind

Prayer and poetry transcend the rationale, logic making mind and rely upon feelings and intuition. After all, whoever thinks that talking to God is like addressing a corporate board room meeting. Whoever worries that their prayer is sufficiently logically laid out. Certain prayers said in church are prayers of petition but it is in the spirit of surrender one makes the request. Prayer is always an act of faith.

Likewise with poetry, it is the sheer act of sitting down to write a poem, having that intention to speak directly to the feeling or thought inside oneself, that can activate the creative impulse. It is with this act of intention that the mysterious part of the language-making brain comes up with words and metaphor, language and sound. Many poets state that when the writing is going well, it's as if is the poem is almost writing itself. As with prayer, poetry is always a heightening of inward experience.

Intimacy with the Muse/Intimacy with God

By and large the praying life, especially private prayer, is one of intimacy with God and needs nothing more that the desire for this intimacy. Prayers asks only for some modicum of trust in the higher power. Some prayers are just that: asking for that ability to trust in God and let the Divine enter one's life.

Poets and readers of poetry also can experience something akin to religious experience when they dive into a more intensely felt inner world.

Grace versus Duende

In religious language this is referred to as grace. Among poets this is referred to as being in touch with the muse, or as the Spanish say, having the duende.

In each, it is an understanding that it is not through willfulness but through opening oneself to something larger than oneself. It is a beseeching that allows the spirit of prayer or poetry into one's life. Both are ultimately acts of surrender.

Solitary Acts of Faith

Both prayer and poetry are essentially intensely solitary acts.

Even when praying with a group of people, the connection one makes to the divine is as an individual. Perhaps the thing that connects them most is that each relies upon a kind of quiet intensity of the spirit and a willingness to enter into a relationship with what the great Welch poet Dylan Thomas called the “holy darkness.”

The closing lines of Dylan Thomas's classic Child’s Christmas in Wales reads: “I said some words to the holy darkness and then I slept.” 

There are a number of famous poets who have written about or to God in their poems, including: I will include links later.

• Rumi
• John Donne
• Gerard Manley Hopkins
• George Herbert
• William Blake
• Emily Dickinson
• W. B. Yeats
• T. S. Eliot
• Rainer Maria Rilke
• Dylan Thomas