People who are fond of grammar would argue that when the word `percentage’ is preceded by the definite article `the’, then the verb is usually singular. It doesn’t really matter if the noun preceding the verb is singular or plural.
*The percentage of students from Delhi is relatively small.
Although the noun (`students’) is plural, the verb that follows (`is’) is singular.
*The percentage of people willing to participate keeps decreasing every year.
When you talk about `a percentage’, on the other hand, it can be followed by a singular or plural verb. It depends on the noun which follows `percentage’.
*A very small percentage of the students are from Delhi.
*I’m told that a small percentage of Padma’s income goes to charity.