Can I adjust the exposure time (shutter speed) in my phone camera?

You cannot adjust it directly, but you can affect the exposure time indirectly in several ways.

In the Scenes shooting mode, certain scene modes affect the exposure time. Sports and Spotlight photo scene modes use short exposure times to enable sharp action shots. Night and Night portrait photo scene modes enable longer exposure times than Automatic or any other scene modes. With those night modes you need to keep the camera very stable to get sharp photos.

In the Creative shooting mode, you can use ISO, ND filter, and exposure compensation settings to affect the exposure time. Also, the flash mode has an impact on the exposure time.