There are a variety of ways to send a file to Web end-point and encode it in the the process. For example, using Invoke-RestMethod -InFile (docs):

C:\PS> Invoke-RestMethod -Uri http://example.com `
  -Method Post -ContentType 'multipart/form-data' `
  -InFile c:\temp\test.txt

However, if we want/need to include one or more files as part of a larger JSON payload, perhaps with other information for each file, we will need to convert the file(s) to Base64.

To do so, we’ll make use of .Net functionality, in particular the System.Convert.ToBase64String method and the System.Web.Script.Serialization.JavaScriptSerializer class (see note).

# define parameters
Param(
    [Parameter(Mandatory=$true, Position=0)]
    [string]$InputFile
)

$content = [System.IO.File]::ReadAllBytes($InputFile)
$base64String = [System.Convert]::ToBase64String($content)

# Load System.Web.Extensions
Add-Type -AssemblyName System.Web.Extensions
$jsonSerializer = New-Object System.Web.Script.Serialization.JavaScriptSerializer
$json = $jsonSerializer.Serialize(@{ content = $base64String })

Write-Output -InputObject $json

# writes: {"content":"dGVzdAOK"}

For a full, proper script, with multiple parameters (writing to a file, copying to clipboard) see this ConvertTo-Base64.ps1 gist.

Note: I chose System.Web.Extensions over the more common Json.Net because I didn’t want to have to download/nuget a dependency; JavaScriptSerializer proves sufficient for this task.