## PowerShell, 21 bytes

 1..$args[0]|%{'*'*$_}

Loops from `1` to input `$args[0]`, each iteration using string multiplication to construct a string of that many `$_` asterisks. Default behavior for the implicit `Write-Output` at the end is with a newline for separator, so we get that for free.

 PS C:\Tools\Scripts\golfing> .\draw-asterisk-pattern.ps1 5
 *
 **
 ***
 ****
 *****
 
 PS C:\Tools\Scripts\golfing> .\draw-asterisk-pattern.ps1 2
 *
 **
 
 PS C:\Tools\Scripts\golfing> .\draw-asterisk-pattern.ps1 7
 *
 **
 ***
 ****
 *****
 ******
 *******