Yes. WinRAR can do this. When the popup screen where you name the archives pops up, where it says "Split to volumes, bytes" on the lower left, manually input 15000000 ...this will make 15mb splits. Also, if you're going for "scene"-style, set compression settings to "Store" (no compression). But if you want to compress go ahead, your question was about splitting.
Oh, and 15000000 is 14.3mb, which is the universally acceptable "15mb" ...if you want to do exactly 15mb, you'll have to get the byte calculator out heh.