Yes, you can use a capital gains loss with the Standard Deduction. Here's a summary:
Capital gains losses can be used to offset capital gains. If your losses exceed your gains, you can deduct up to $3,000 of the excess loss against your ordinary income each year.
f your capital losses exceed your capital gains, the amount of the excess loss that you can claim to lower your income is the lesser of $3,000 ($1,500 if married filing separately) or your total net loss shown on line 16 of Schedule D (Form 1040), Capital Gains and Losses.
This deduction is separate from the Standard Deduction, meaning you can claim both on your tax return.