Will this Nikon lens fit on a more current Nikon DSLR?

I have a telescoping lens that my mom bought for me in 2003 for my Nikon camera. It was a camera that used film instead of being a digital camera. Will the telescoping lens (the writing on it says 70-300mm, 1:4 - 5.6 D, DL Macro Super) made by Nikon fit on a DSLR camera?

The Nikkor 70-300 mm lens is an excellent one, but my guess is that your lens is a third party lens ("super macro" is the give away), probably made by Sigma

Actually it is NOT a telescoping lens. It is called a zoom lens

That said, if you buy a better than entry level dSLR, you will be able to use any auto-focus lens made to fit any Nikon camera after about 1977.

If you are planning on buying an entry level dSLR, then you will need to use lenses that are either Nikkor AF-S lenses or lenses that have on-board auto-focus systems.

The lens you mentioned is an economical lens that cost under $225 new, so probably don't have such an auto-focus motor

It's the old sigma 70-300. Yes that will fit but you need a d90/d7000 or better for it to autofocus.