Welcome to iMore! You can't move photos to iCloud and remove them completely off of your device but you can use iCloud Photo Library to minimize the amount of local storage that your photos use by keeping full resolution photos in iCloud and lower resolution copies on your device. The process is seamless and you always have access to your full res photos as long as you have an internet connection. To set this up, go to Settings > iCloud > Photos, toggle iCloud Photo Library on if it isn't already, and make sure Optimize iPhone Storage is checked.
If you truly want to remove your photos from your phone you'll want to utilize a third party backup service like Dropbox, iCloud, Amazon Prime Photos, OneDrive, or something along those lines.