Turn the shirt inside-out, and use scissors to cut a tiny square of fusible tape just slightly bigger than the cigarette burn. Stick it directly on the hole.
Cut a small piece of fabric from the inside hem of the shirt or from one of the seams to use as your patch.
Turn the shirt right-side out. Add a dot of fabric glue onto the cigarette burn.
Press the tiny patch onto the glue, and allow it to set overnight. Run an iron set on medium heat over the patch to set it.