According to this post at AskUbuntu, your adapter is natively supported since Ubuntu 15.04 or Kernel 4.2. Since it isn't working, we are left with two main options, but both require an active internet connection at some stage.
First option would be to check for any proprietary drivers to install with software-properties-gtk (sudo apt-get install software-properties-gtk if you don't have the package - doesn't come by default for elementaryos).
Second option (not recommended) would be to manually compile and install the driver from GitHub for your current kernel version. I'm not sure that would work since your kernel is supposed to bundle it already. The 1st and 2nd commands can be skipped if you download and extract the .ZIP code.
sudo apt-get install linux-headers-generic build-essential git
git clone https://github.com/art567/mt7601usta
cd mt7601usta/src
make
sudo make install
sudo mkdir -p /etc/Wireless/RT2870STA/
sudo cp RT2870STA.dat /etc/Wireless/RT2870STA/
sudo modprobe mt7601Usta
(!) Note that the author of the post states that you should **re-compile and re-install the driver when you update your kernel from now on:
cd mt7601/src
make clean
make
sudo make install
sudo modprobe mt7601Usta
You may also call sudo make uninstall to remove the driver at a later stage.