Yes. On an iPhone, the simplest built-in method is to shoot a Live Photo, then open it in the Photos app, swipe up, and choose Long Exposure. This blends the frames from the Live Photo to create a smoother, blurred-water look.

For better control, you can also use a third-party camera app that allows longer shutter speeds or manual exposure settings. In brighter light, a long exposure can easily overexpose the image, so an ND filter and a small tripod/phone mount can help a lot.

A tripod is especially useful because the water should blur while the rest of the scene stays sharp. If the phone moves too much, the whole image may soften. Also note that scenes with moving subjects besides the water may not look natural in a single long exposure; some examples like sharp fish with blurred water may be composites or blends of multiple images.

So: yes, it’s possible, and the easiest path is Live Photo + Long Exposure; for more control, use a manual camera app plus stabilization and possibly an ND filter.