Can I contribute to my Roth IRA in December and then again in January?

Traditional and Roth IRA contributions are linked to the tax calendar.

The 2021 IRA contributions can be made anytime from January 1st 2021 until the day tax returns are due in April 2022.

The 2022 IRA contributions can be done anytime from January 1st 2022 until the day tax returns are due in April 2023.

During the period between January 1st each year and the day tax returns are due in April you have to specify when you make the contribution which year the contribution applies to.

Bedsides procrastination, some people wait until after the end of the calendar year to make their contribution due to tax reasons. Some know they will be near the maximum income for deductiblity or even the ability to contribute, and want to wait until they fill out their tax forms before make the contribution. Others will use the refund they get to make the contribution.

It is actually possible to contribute to both the 2021 and 2022 IRA on the same day. Though I suspect that doesn't happen very often.

You don't want to wait until the last day to establish an IRA because sometimes that can take a day or two, but subsequent contributions made online are essentially instantaneous.

Note: A 401(k) contribution has a deadline of December 31st.