First we need to install the Azure PowerShell module from http://go.microsoft.com/fwlink/p/?linkid=320376&clcid=0x409

Then open PowerShell and follow the below commands:

#Get your subscription file - The browser will open, you will need to login to the Azure Subscription and finally it will download the <subscriptonname>.publishsettings file
Get-AzurePublishSettingsFile

#Connect to your Subscription
Import-AzurePublishSettingsFile -PublishSettingsFile "full path to downloaded file"
Source: http://www.e-apostolidis.gr/microsoft/connect-powershell-to-azure/