Sure. Sort of. You can link SOME social media platforms via their own functionality. Ie Twitter and Facebook talk together no problems.
Now that FB own IG you can also set up IG to post to FB directly also.
But if you want to do them all you may find the best way is to use a 3rd party program like Hootsuite of tweetdeck.
Jef Lippiatt Owner at Startup Chucktown
I would also recommend looking at Buffer (which is similar to Hootsuite).
Another alternative to checkout is IF or IFTTT also known as "If This Then That". It is a mobile app that has tons of easy to setup integrations. It can work around some of the issues mentioned above (like turning a picture into a link - it will keep a picture intact across networks for example).
There is 1 counterpoint I want to mention. There are several sources that are telling people and businesses not to use functions like this for 1 reason. Each social network has its strong points and weaknesses. You should not only tailor your content to your audience, but also the specific social network.
Remember focused content directed toward your target audience is more important that frequently blasting out the exact same content across Facebook, Twitter, Instagram, Pinterest, etc. If you are sharing the same content on all channels why would anyone follow you on more than 1 channel?