should of asked me to join vs should have asked me to join

Some examples from the web:

• AUSA Sandoval asked me to join.
• They've even asked me to join their craft circle.
• She asked me to join her.
• He asked me to join him.
• And then Mrs. Frederic asked me to join the warehouse.
• They asked me to join them, but my dad's kicking off about it.
• This young man asked me to join the liberal movement.
• Bree asked me to join her company.
• First, Johnny has just asked me to join his tribe.
• He asked me to join the campaign to stop the illegal fishing of sharks.
• They asked me to join in the alumni dinner.
• They've asked me not to join up, sir.
• No. He's asked me to join him in Massachusetts, - as a partner.
• I did some freelance work for them a few months ago and they were impressed, so they asked me to join on a more permanent basis.
• I'll never forget where I was when Tristafé asked me to join the front row.
• But the third day, the kid asked me to join his gang.
• Mr Prettiman has asked me to join him and Mrs Prettiman in establishing his new world.
• AJS asked me to join them full-time.
• You have dinner with him alone at Lemont and you've never once asked me to join you.
• Why? Last time she was here, she asked me to join her firm.

Some examples from the web:

• AUSA Sandoval asked me to join.
• Malta and Cyprus have asked to join the Community.
• Do you think I should have asked them to join in?
• They've even asked me to join their craft circle.
• She asked me to join her.
• He asked me to join him.
• And then Mrs. Frederic asked me to join the warehouse.
• They asked me to join them, but my dad's kicking off about it.
• This young man asked me to join the liberal movement.
• Bree asked me to join her company.
• First, Johnny has just asked me to join his tribe.
• He asked me to join the campaign to stop the illegal fishing of sharks.
• They asked me to join in the alumni dinner.
• The implementation of national projects has been delayed in all Member States that have asked to join the Schengen area, except one.
• They've asked me not to join up, sir.
• I have asked Caroline Hope to join us.
• No. He's asked me to join him in Massachusetts, - as a partner.
• I did some freelance work for them a few months ago and they were impressed, so they asked me to join on a more permanent basis.
• I'll never forget where I was when Tristafé asked me to join the front row.
• But the third day, the kid asked me to join his gang.