While we have an action with a character holding a microphone, the character is animated to sing (you can find it under "sing" in the "Actions" tab search bar. If you just want your character to hold the microphone and/or talk instead of sing you can still achieve this with an easy workaround!
In the "Actions" search bar, type "holding", then scroll down a bit until you see the action "holding pole".
Once your character has assumed the action, simply place a microphone prop in your character's hand and send the prop backward by using the "send backward" option in the toolbar (as shown below).
The character will now appear to be holding the microphone. You can then add "talk no lip sync" expressions if you want the character to just move his/her lips or even attach dialogue if you want him/her to speak specific lines.