Recently one of my friend asked me below mentioned question.
How can I track how many clicked the referral link via my Instagram bio?
I wondered there should be an easy way without setting up your website and manage it via google analytics. It was a quick search and easy use. The answer is use bitly.com and its Free.
The use case explained below, Say you have an Instagram account and you are promoting a brand. For example purpose you are promoting www.nike.com
Login to bitly via your Facebook or Twitter account. You can also create a new signup. I created a new signup. Once you login you will see below screen. 
Next you click on top right orange button Create Bitlink. You will see the screen below. First you paste the long link of your referral in the box which says “PASTE LONG URL”. Example: www.nike.com Click on create button on the bottom of the page.
You will moved to another page displayed on the right side EDIT BITLINK. On Edit page update the “TITLE” box as some meaningful name – Instagram (Any social media site you want to track the source from). Then click Save.
That’s it. You are done. Your link is ready for tracking. See below.
Now it is time to test. Copy the link and paste it into your Instagram bio. I tested it for my site and below is the result on your dashboard.
The same with full screen and additional dashboard information for multiple links.
If you have any further question add it on the comments below. I will try to answer them.
Happy Tracking!!!
Vikram Shetty 