Yes, you can enlarge it somewhat, but no software can truly create missing detail. Photoshop and dedicated resizing tools can make an image look smoother when scaled up, but they won’t turn a low-resolution photo into a genuinely sharp high-resolution one.

Specialized plugins such as ON1/Perfect Resize or Alien Skin Blow Up were mentioned as doing a better job than basic resizing, especially for making large images look smoother. That said, results depend heavily on how much detail is in the original image.

For a website background, you may not need as much resolution as you think. One community answer notes that a web background often doesn’t need to be larger than about 1024×768, and keeping file sizes reasonable matters because visitors have to download the image.

So the practical answer is: if your photo is already around common screen-background dimensions, try it first before upscaling. If it looks soft, a high-quality resizer may help a little, but there’s a limit to how far you can push it.