The short answer is no. 72 is what the camera took the picture in so you're pretty much stuck with that unless you use photoshop to resize the image.
And when you resize the image (by using the Image Size command under the EDIT menu), the key is to uncheck the box next to "Resample Image". Then simply enter in 300 in the Resolution box. Doing it this way will simply size down the image to squeeze the pixels close enough so that it increases from 72 dpi (or more appropriately ppi) to 300 dpi.
Think of it this way. There are 72 pixels per inch. In order to increase that to 300 pixels per inch without resampling (creating pixels), you'll need to squeeze the pixels tighter together thus resulting in a much smaller image inch-wise. The resulting size will be about a 7.5x11 inch image.
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