Yes, there are several ways to see what tasks have been assigned to you in Procore.
Users with 'Read Only' level permission or higher on the company's Portfolio tool can click the My Open Items link to view a list of all the tasks that have been assigned to you in the company's projects. See View My Open Items in the Portfolio Tool.
Project Home: My Open Items
User's with 'Read Only' level permission or higher on the project's Home page can scroll to the My Open Items area. If you are not seeing an item in your My Open Items list, see Why are items assigned to me not showing up in My Open Items on the Project Home page?
User's with permission to the company's Reports tool can view the Assignment Report that will break down all items assigned to specific user. Among other things, the report provides project name, tool, link to the item, and the status of that item. This is a great way to manage all of your action items across your different projects.