Here are some phrases and expressions for inviting in English.
See also: Free-English-Study: Inviting
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Do you want to . . .
Do you wanna . . . (informal)
Would you like to . . . (more polite)
How about (V+ing) ?
How would you like to . . .
Speaking Situations : Inviting
See also :
Speaking : Accepting and Refusing
Business : Invitations
Textbook : Touchy Situations, Chapter 7, New Interchange 1, Chapter 4, English Knowhow, Book 1, Chapter 3