Yes, the poem makes it clear that an actual raven does fly into the speaker's chamber. In the seventh stanza, lines 1 & 2, the speaker says, "Open here I flung the shutter, when, with many a flirt and flutter, / In there stepped a stately raven of the saintly days of yore." This is telling the reader that the raven did fly into the speaker's chamber.
The speaker does think that the raven talks to him ... this is what he is imagining.
Your question can be answered in two different ways.
Yes, there is a real raven and it really can talk. At least it can say one word. It may have gotten lost in the storm somehow and was seeking shelter in a human domicile, indicating that it was probably a pet. The poem calls for "a willing suspension of disbelief." We are supposed to believe everything in "The Raven" is true and is really happening, and even to believe that the raven is still sitting on the bust of Pallas casting his shadow on the floor.
No, there is no real raven. Nothing in the poem is really and truly "real." Everything is entirely imaginary because it is, like Poe's short stories, a work of creative imagination. Poe himself explained how he composed the poem out of thin air, so to speak, and even why he chose to write about a lost love and to give her the name Lenore. He probably poured real emotions into a totally imaginary poetic narrative.