No, but I see why you might think so.
In some ways they are analogous:
a Sprint (which is a clearly separated period of development work towards a specific goal)
is to the Set of Stories Completed Thus Far (which is a description of all the development work done so far)
as a Branch (which is* a clearly separated location in a repository for source code under development for a specific purpose)
is to the Trunk or Master (which is* the source code that reflects all the work that's been done so far)
*assuming one is using a model in which development work for features is done on branches, and branches are merged back to master as each feature is completed. There are other models, but this one is pretty common.
And if this is the model you're using, then during a sprint, there will be one or more active branches; and at the end of the sprint, assuming that you completed all the planned work, all those branches will have been merged back to master.
As CodeGnome said, the workflow you use to manage source code during development is very different from the methodology you use for project management. If you've spent most of your time so far as a solo developer, it can be hard to understand that there is anything else involved in development methodology besides how you manage and manipulate your source code.
Instead, think in terms of how you are going to plan, divide up, and manage the work required to complete the project. That's where Sprints come in.