Is it permissible to take a percentage in exchange for finding a job for someone?

What you are doing, mediating between an employer and an employee, is called "brokerage," and it is permissible in Islamic law. It falls under the category of "Ja'alah" (commission/reward), and there is no harm in taking a fee for it. The fee you receive for your mediation must be known and specified, such as a certain amount, and it is not permissible for it to be unknown.

Some jurists consider a "Ja'alah" with an unknown amount to be permissible, for example, if the employer says: "Sell my garment for such-and-such, and whatever exceeds that price is yours." Based on this, there is no objection for you to search for a job for your friend in exchange for a percentage that he pays you when the job is secured.

However, it is preferable for you to agree with him on a known amount that he will pay you upon securing a suitable job.