Can I deduct Turbo Tax cost for 2019 if I took standard deduction and did not itemize deductions?

No.

Actually, no, ether way, standard or itemized.  That particular itemized deduction* was eliminated with the new 2018 tax law. 

*and all other "misc. itemized deductions", subject to the 2% of AGI threshold.

If you are self-employed, you may be able to deduct accounting and tax software as a business expense.  The ability to deduct business expenses on schedule C is completely separate from the ability to deduction personal expenses on schedule A.

The itemized deduction for "miscellaneous itemized deductions" on schedule A was eliminated in 2018 tax reform.