If you have an iPhone 12, 13, or SE 3rd generation with 5G service, yes you can. Otherwise no, you will either need to find WiFi or use a computer to upgrade.
Ask a friend or relative who may have WiFi or a computer you can use.
You can also go to an Apple store and ask to use one of their computers.
Update your iPhone, iPad, or iPod touch
• If you have an iPhone 5S or 6/6plus, the highest you can update to is 12.5.5
• If you have an iPhone 6S through 13, you can update to 15.6.1
Go to Settings > General > Software Update.
Update your iPhone, iPad, or iPod touch using WiFi -
Update your iPhone, iPad, or iPod touch - Apple Support
Update using your computer -
Update iOS on iPhone - Apple Support