Yes you can, but this will result to installing many files to your system and increasing your disk usage and also cpu/ram usage.
1. Install the Desktop Environment and VNC server
Usually an Ubuntu VPS does not come with a graphical desktop environment or a VNC server installed, so you must first install those. To use the minimum disk space and minimum resource I used Xfce desktop environment and TightVNC myself.
sudo apt install xfce4 xfce4-goodies tightvncserver
To complete the VNC server's initial configuration after installation, use the vncserver command to set up a secure password.
2. Configure the VNC Server
You should configure vnc so that it first starts the desktop environment then the vnc service. Firstly, kill the vnc server that you started in the first step:
vncserver -kill :1
Prepare the startup file
Put these lines into the file:
Make sure the file is executable
sudo chmod +x ~/.vnc/xstartup
Now start the vnc server and you are ready to use it:
You can use any windows vnc client to connect to your server from port 5901. Personally I like mRemoteNG to manage multiple servers.
To setup vnc so that it starts automatically after each restart, you need to set it up as a service. You can read the details of these step and the setup as a service from this page which I used as reference: