Is there any way to check for digital signature on a file programmatically in Powershell?

Try the Get-AuthenticodeSignature-cmdlet

(Get-AuthenticodeSignature "C:\windows\explorer.exe").Status -eq 'Valid'

True

(Get-AuthenticodeSignature "D:\notes.txt").Status -eq 'Valid'

False

You could simply call signtool.exe to verify the result.