You can create an Automator action. Automator was created to deal with these tedious repetitive tasks (the kinds of things computers were made to handle.)
First, create a new folder on your mac to be the destination for screenshots and use the "defaults write com.apple.screencapture location" command (just as in leroydouglas' example above) but set your own folder; don't use the Photos library as the folder. Photos wants things in that Photos library organized in a particular way. The Automator action will tell Photos to import your folders to they go into the library in the way Photos requires.
- Launch Automator (it's in your Applications folder)
- It will likely prompt you for the type of Automator action you want to create, but if it does not, select "File" -> "New" and the type of action you want is a "Folder Action"
- The top of your new action (the empty panel on the right side of the Automator window) will start with "Folder Action receives files and folders added to" and you need to pick the "Choose Folder" menu, pick "Other..." and select a folder (you'll find the familiar file navigator window and you can also tell it to create a new folder.)
- In the far left column (under the "Library" section) pick "Files & Folders"
- In the next column to the right, grab "Get Folder Contents" and drag that with your mouse into the blank action list on the right (I'll give you a screenshot of this). (That's the first step done ... now we just need to add it to Photos)
- In the far left column, this time pick "Photos"
- In the next column to the right, grab "Import Files into Photos" and drag that with your mouse to the action list and drop it below the "Get Folder Contents" step. They will automatically link up.
- You have a few choices, as to where these go in the Photos app. While you can choose "Import without adding to album", that's a messy choice. I created an Album in Photos called "Screen Shots" and in the Automator action step, I chose "Add to existing top-level album..." and then chose the "Screen Shots" album.
- Select "File" -> "Save" and give the automator action a name (I used "ScreenShots to Photos")
- Quit Automator
That's it... now anytime an screenshot shows up in that folder, it will get imported to Photos in the album or your choice.
Automator wont delete the images from that designated Finder folder (that's up to you) but it will (by default) check for duplicates and wont re-import a duplicate. So if you don't need the individual screen-shot files after you import them, you might want to empty that folder to trash.
Your Automator action should look like this when you're finished. Note that I've circled a few things... don't forget to set the folder you want to use as the trigger... and the destination location within Photos (e.g. if you send them all to an album.)

This will probably "just work". But what if it doesn't? What could have gone wrong?
If the Automator action doesn't work, it may be that you've disabled them. To check, open Finder, navigate to the folder you've selected to trigger the action, and right-click (or control-click) to open the pop-up menu.
Near the bottom of the pop-up menu, pick "Folder actions setup..."
The first thing to verify is that the "Enable Folder Actions" check-box is ticked on.
Next, verify that your designated folder (in my example it's the "ScreenShots" folder is is on the list of "Folders with Actions" (left column) that actually have an action associated with it.
Lastly, make sure your Automator action (in my example it's "ScreenShots to Photos" is in the "Script" list (right column) and that the tick-marks are checked meaning they are switched on. (you could turn the action off just by un-checking it... or highlight the step and hit the "-" icon at the bottom of the column to delete it.

That's it!