Can I use the "SDcard to Lightning Connector" to put photos on my iPhone?

No

"

This accessory is compatible with the following:

• iPad
  4th generation
• iPad mini"

http://store.apple.com/us/product/MD822ZM/A/lightning-to-sd-card-camera-reader

I already answered the question.

Why? It's the same iOS, the same connector (Lightning) and the same hardware like an iPad mini, so why doesn't Apple allow users to connect with an sd-card????

hpp23 wrote:

Why? It's the same iOS, the same connector (Lightning) and the same hardware like an iPad mini, so why doesn't Apple allow users to connect with an sd-card????

We are not Apple, so we cannot tell you, we are users just like you.