• "Can I ask you a question?" is commonly used to request permission politely and appropriately.
• "Shall" is used to make offers or suggestions, not typically for asking permission.
• "Will" is used to express willingness or intention, which doesn’t fit the context of a polite question.
• "Might" is more formal but is rarely used in everyday speech for such requests.

Thus, "Can I ask you a question?" is the most suitable option.