Below is the snippet for using Power Shell to execute list of SQL scripts under a specific folder. I use this script in Octopus deployment to deploy database changes (* for this particular case, we don’t use Code First therefore we don’t use Migrate.exe)

# Connection String
[string] $ConnectionString = "server=MyDBServer;database=MyDatabase;user id=Myuser;password=Mypassword;trusted_connection=true;"

#The folder where all the sql scripts are located
[string] $ScriptPath= "C:\Octopus\Applications\SQL2014UAT\Powershell Deployment\Scripts"

# Go to every single SQL files under the folder
foreach ($sqlFile in Get-ChildItem -Path $ScriptPath -Filter "*.sql" | sort-object)
{
    $SQLQuery = Get-Content "$ScriptPath\$sqlFile" -Raw
    
    ExecuteSqlQuery $ConnectionString $SQLQuery 
}

# executes multiple lines of SQL query
function ExecuteSqlQuery ($ConnectionString, $SQLQuery) {
    # Use GO to separate between commands
    $queries = [System.Text.RegularExpressions.Regex]::Split($SQLQuery, "^\s*GO\s*`$", [System.Text.RegularExpressions.RegexOptions]::IgnoreCase -bor [System.Text.RegularExpressions.RegexOptions]::Multiline)

    $queries | ForEach-Object {
        $q = $_
        
        if ((-not [String]::IsNullOrWhiteSpace($q)) -and ($q.Trim().ToLowerInvariant() -ne "go")) 
        {            
            $Connection = New-Object System.Data.SQLClient.SQLConnection

            Try
            {
                $Connection.ConnectionString = $ConnectionString
                $Connection.Open()

                $Command = New-Object System.Data.SQLClient.SQLCommand
                $Command.Connection = $Connection
                $Command.CommandText = $q
                $Command.ExecuteNonQuery() | Out-Null
            }
            Catch
            {
                echo $_.Exception.GetType().FullName, $_.Exception.Message
            }
            Finally
            {
                if ($Connection.State -eq 'Open')
                {
                    write-Host "Closing Connection..." 
                    $Command.Dispose()
                    $Connection.Close()        
                }  
            }
        }
    }
  }

Alternatively if you have SMO, PS extensions and the snap in then you can use simpler script below. For the pre-requisites for invoke-sqlcmd is here

Get-ChildItem -Path "C:\Octopus\Applications\SQL2014UAT\Powershell Deployment\Scripts" -Filter "*.sql" | % {invoke-sqlcmd -InputFile $_.FullName}