I'm copy and pasting from illustrator the Wild Turkey logo into my photoshop file as a smart object.
While doing so the logo appears to have very pixelated edges.
Like this here:
Is there a way to prevent the pixels ?
Make sure the resolution is the same in both apps.
Or you can simply Save your document in Illustrator, then open that Illustrator document with Photoshop, and then you will be prompted to choose the way the vector document is rasterized so that you get a Photoshop document that is exactly what you want. Then drag-and-drop the logo from the new Photoshop document to the one you are working on.
Instead of pasting the file directly in, you could use Illustrator to export it as a High Quality PNG file and then import it into Photoshop. If this isn't high enough for you, you will need to adjust the Photoshop document's settings to increase the resolution.
The problem likely isn't based in Illustrator as Illustrator produces vectors (equations about lines and shapes and colours etc that can scale and shrink) as opposed to Photoshop's bitmaps (coordinate graphs of colours, not scaleable without pixelation or graininess)
You'll get the best quality when you paste as shape. It looks like you could do it with your object, since it's monochromatic.
Make sure it's a compound object or group of objects without vector effects applied, expand the appearance if necessary, copy to clipboard and paste in Photoshop. Select "Paste as: Shape Layer".
Now you can control the alignment of your object to the pixel grid in Photoshop, and even edit specific path points if necessary.