Yes, but you will have to be careful about it.  Unlike private foundations that have to have a scholarship program approved in advance by the Internal Revenue Service, public charities may make scholarship grants without prior approval.  But they should be aware of the issues that the IRS asks about on the Form 1023 application for recognition of exemption (for both public charities and private foundations) and in approving private foundation programs.

The scholarship awards should be based on objective and nondiscriminatory criteria such as academic qualification and/or financial need.  It should be broadly advertised and operate with a written application process.  The pool of applicants should be large enough so that the program is not being operated primarily for the benefit of a small group of individuals (i.e. your members).  You don’t want to give extra credit for children of club officers  or other activists.  Selections should be made by an independent selection committee whose members cannot personally benefit from the selections.  You should retain records of the winners and how they use the scholarships.  You should have specific criteria for eligibility to obtain renewal grants if you operate the program beyond freshman year.

If you are going to limit the pool to children and grandchildren of members, you ought to take a few additional pointers from the issues facing corporate foundations that have scholarship programs for the employees of the corporation and their children.  You don’t want to use the scholarship program as a recruitment tool for new members of the club.  You don’t want the IRS claiming that the program is a private benefit of the members.  And you may want to limit the number of scholarships so that it is not an automatic membership benefit for any member who has an eligible child or grandchild.  Corporate foundations, which can’t use the program as additional compensation for employees, must limit the number of scholarships to 10% of all eligible candidates or 25% of those who applied.  If your pool is open to applicants other than members’ relatives, you may not need to be so concerned with the number of relatives awarded grants, but you probably want to be sure that you make grants to unrelated applicants as well.