You should not.
If you are a non-US person and own a single-member LLC the Form W-9 does not apply to you. The only exception would be if you have elected C Corporation status for your single-member LLC, in that case, for tax purposes, it is no longer a disregarded entity but instead a corporation.
The correct form to fill out is the Form W8-BEN. You can read my instructions on how to complete Form W- 8 BEN here.
In order to complete Form W-9 you would have to sign the following certification:
I often speak to clients who insist their LLC should be treated as a U.S. person because it is formed in the LLC, but look at the section where U.S. person is defined:
It would not be unreasonable to think that a foreign owned single-member LLC may still fall under “company” in the second bullet point.
Unfortunately, this is settled in a later part of the form instructions:
This is not truly unfortunate, as any income for which the W-9 is appropriate, would also mean that the income was taxable in the United States as it was earned by a U.S. person.
If you are asked to complete a Form W-9, you should inform them this is not the correct form for you and ask to complete a Form W-8 BEN instead.