Brinkley (undisclosed) was placed on injured reserve Monday, Tori McElhaney of the Falcons' official site reports.
Brinkley signed a one-year contract with the Falcons on Monday.
Brinkley was signed to the active roster Saturday.
The Titans waived Brinkley on Wednesday, Jim Wyatt of the team's official site reports.
The Titans activated Brinkley from the reserve/COVID-19 list Sunday, Jim Wyatt of the Titans' official site reports.
The Titans placed Brinkley on the reserve/COVID list Tuesday, Jim Wyatt of the team's official site reports.
Brinkley will likely miss this week of practice due to a groin injury, Paul Kuharsky of 104.5 The Zone reports.