Informatica itself neither supports Jenkins directly in any way, nor do they keep anyone from using it.
It depends on what integration you want to achieve.
I don't know Jenkins myself, so my opinion about this is purely theoretical and very generic.
Either way, this topic has been discussed numerous times over the past years. I won't bother repeating all those threads here, you can please search them yourself. Then we can discuss strategies and/or details.
Informatica PowerCenter (PC) is not certified nor is it integrated to run with any external version control system like Jenkins.
But, Informatica Big Data Quality/Big Data management supports CICD. (from 1022)
Informatica document Sample Automated Integration Process has sample processes that you can refer to Sample Automated Integration Process
For Jenkins related queries, on how to use it with CICD refer Continuous Delivery with Informatica BDM
You can also refer Deployment best practices in BDM for more details on deployment options.
Hope this helps you get overview of the CICD process with Informatica BDM/BDQ.
PowerCenter (PC) is not certified nor was it designed to be integrated in order to run with any external version control system like Jenkins.
Even though its not certified it doesnt mean that it will never work, it just means that it was never QA tested with Informatica
As a potential workaround, you might be able to create some scripts that will execute export/import of XML of the session/mapping objects. Then use Jenkins to version control the XML files.
So the basic idea is to store the XML files in GIT and retrieve them later (through Jenkins) for import back into PowerCenter. There is no out of the box integration between PowerCenter and these tools. Export/import through XML is supported by us, however, you need to develop the scripts to accomplish these tasks.
Also Assuming that you might have an independent Jenkins server, which is used by the whole enterprise. Assuming that this server does not contain the PC software on it. As long as you are able to install only the PC command line utilities on this server, you can still execute these scripts (deployment and execution scripts) from this Jenkins server, where Informatica installation is not existent.
One additional note to Gabriel's good response:
The so-called "Command-Line Client" essentially is a stripped-down server installation which can be used to run the command-line tools (in your case, pmrep and maybe pmcmd) on almost any machine in your network. The use case is for shell scripts, batch files, PowerShell scripts, VB programs, and whatever which can run anywhere and yet run pmrep, pmcmd, infacmd.sh and the like without having a "full" server installation.
The command-line client doesn't count in terms of CPU cores for your license, it's free to use.
You can request a download link from Informatica Shipping (e.g. via Global Customer Support), just tell them for which operating systems you need the download links.