Apparently, Gandalf says: "Gwaihar − go!"
The aforementioned moth does not appear in the books, so an answer from book-canon is non-existent.
I checked multiple scripts of Peter Jackson's The Fellowship of the Ring online, and I've gotten varied results.
The iMSDB script (my first Google search result):
EXT. ISENGARD -- NIGHT
Low angle...looking up at ORTHANC...the tower of Isengard,
gleaming in the moonlight. The camera rises to reveal the
once beautiful gardens are not a pitted wasteland...with
smoke and fire billowing out of numerous tunnels and vent holes that litter the forecourt
of ORTHANC. Strange guttural chants echo up from deep
underground. The camera is rising...a small moth flutters
into shot...and leads the camera towards the summit or
Orthanc. Gandalf lies slumped against the wall at the very
top of Orthanc, surrounded by a sheer 500 foot drop. He
looks Weak and Frail...and is seemingly asleep. The MOTH
flutters close to Gandalf. His hand suddenly moves at
lighting speed and SNATCHES THE MOTH. Gandalf brings his hand
close to his face and opens it. The moth sits on the palm of
his hand as Gandalf mutter strange words in a foreign tongue.
Close on: THE MOTH'S face... seemingly listening.
The Age of the Ring script (from which I based my answer on):
Isengard is now surrounding by deep ravines in the ground, which glow orange. Wooden structures stand around the ravines. Inside the ravines, wooden walkways and pulleys have been built, where hundred's of orc are working. A moth flies over the caverns to the top of Orthanc, where Gandalf sits dozing. As it flies past him, he quickly reaches out a hand and gently grabs it.
GANDALF: (whispering to the moth in an unknown language) Gwaihir go! Gwaihir
The moth flies off.
And from Tolkien's Gateway entry of Gwaihir:
2001: The Lord of the Rings: The Fellowship of the Ring:
Gandalf whispers "Gwaihir" repeatedly to a moth that arrives at Isengard. Later, Gwaihir rescues Gandalf from Isengard, and carries him to safety.
You can watch the scene and judge for yourself whether Gandalf says "Gwaihir" or is just talking gibberish. I, personally hear only a very muffled "Gwaihir", but the "go" is there.