Yes, invite is a Scrabble word!

Verb

1. Increase the likelihood of

2. Invite someone to one's house

3. Give rise to a desire by being attractive or inviting

4. Ask someone in a friendly way to do something

5. Have as a guest

6. Ask to enter

7. Request the participation or presence of

8. Express willingness to have in one's home or environs

Noun

1. A colloquial expression for invitation