Lura is right. The first place to go for Carroll Y-DNA is the Carroll project. And you should test at least 67 markers. Anyone who has tested less than 67 markers should upgrade to 67.
One of the things we have learned from Y-DNA testing is that practically all surnames have multiple unrelated origins. And the name Carroll is no exception. These multiple origins can be identified with SNPs (single nucleotide polymorphisms) and markers. My job is to figure out what category you belong to. The results table for the Carroll project has 14 categories to differentiate participants by origin.
66 Carrolls have tested 67 markers. Of these 60% fall into categories that have known historic origins. The men in these categories have Y-DNA that matches a set of surnames (not just Carroll) that are said to be related in ancient pedigrees. These categories are shown below, together with suggestions of historical projects at FTDNA that these participants should join.
•15 in Clan Colla. These participants should join the Clan Colla DNA project.
•11 in Ely Carroll. These participants should join the Ely Carroll DNA project.
•10 in Niall of the Nine Hostages. These participants should join the M-222 Northwest Irish DNA project.
•2 in Irish Type II/South Irish. These participants should join the South Irish DNA project and the Eoganachta DNA project.
•1 in Brian Boru (L21, Z253, L226). These participants should join the Brian Boru project.
There is a 40% chance of not falling into a known historical origin. These people, however, can still learn from their Y-DNA testing. One of the most valuable thing to learn is the names and email addresses of people with similar DNA. There also are non-historical projects that these people can join to learn more about their origin.
Only men have DNA with a Y-chromosome (Y-DNA). The big advantage of Y-DNA is that it is inherited down the male line like surnames. Women with a certain surname often find a male with the surname to test, such as a brother or male cousin. My wife is a Carroll and we found a male second cousin (198624) who agreed to testing.
I myself have Clan Colla DNA, so I am in the Clan Colla project with 12 Carrolls (not all of the above 15 Carrolls have joined the Clan Colla project, yet).
The easiest way to find a DNA project is to Google it.