As noted in the comments by @BryanKrause, the percentage of cases stratified by vaccination status should not be used as a metric of vaccine effectiveness. If you are interested in vaccine effectiveness, please refer to other Q&As on this site.
This dashboard from the US Centers for Disease Control and Prevention:
Monitor[s] rates of COVID-19 cases and deaths by vaccination status, data are reported from jurisdictions that link case surveillance data to immunization registries to identify the vaccination status of people who test positive for COVID-19
Unfortunately, the data was last updated in October. Also, the data presented is normalized to percentage of the population. However, the raw data is available. If we aggregate the data by week, we can see the actual numbers.
Week Vac Infections Vac Population Unvac Infections Unvac Population Per Vac
Apr 04-Apr 10 13009 64616655 998210 389001215 1.3
Apr 11-Apr 17 15374 76837234 951745 362335790 1.6
Apr 18-Apr 24 16620 91090098 762690 344546755 2.1
Apr 25-May 01 17498 106726671 665515 330087090 2.6
Aug 01-Aug 07 202679 203738268 1579155 238857775 11.4
Aug 08-Aug 14 228938 205588232 1762760 231557335 11.5
Aug 15-Aug 21 251137 207515979 1867915 224857815 11.9
Aug 22-Aug 28 267330 209711985 1911810 218552875 12.3
Aug 29-Sep 04 255902 212117207 1671295 212555660 13.3
Jul 04-Jul 10 30659 194649540 341970 260628810 8.2
Jul 11-Jul 17 56417 197420288 571990 256951840 9.0
Jul 18-Jul 24 99759 199545230 909635 252483390 9.9
Jul 25-Jul 31 156155 201728086 1309425 246174005 10.7
Jun 06-Jun 12 9711 174913860 168920 277511855 5.4
Jun 13-Jun 19 10315 179493568 170675 272843845 5.7
Jun 20-Jun 26 13100 185656716 177710 268640785 6.9
Jun 27-Jul 03 19020 191081150 239950 263884500 7.3
May 02-May 08 15273 120508742 538085 319074225 2.8
May 09-May 15 13398 134112747 451595 310922840 2.9
May 16-May 22 12303 147548191 333750 298347905 3.6
May 23-May 29 10441 158873155 243670 288633585 4.1
May 30-Jun 05 9511 167968184 193225 282740405 4.7
Sep 05-Sep 11 248622 214805454 1467545 208199840 14.5
Sep 12-Sep 18 237507 217660765 1259850 203524000 15.9
Sep 19-Sep 25 208476 220027372 1007055 199777100 17.2
Sep 26-Oct 02 203707 222693630 860630 195935955 19.1
Thus, at the last time point with available data, 203707/(203707+860630) = 19.1% of all cases were among fully vaccinated individuals.
A major caveat from the foot notes is that not all jurisdictions report the required data.
The New York Times has an article about this dataset.
Some US states, such as New York, Virginia and Minnesota have provided subsequent datasets, but I was unable to find a tracker that aggregates all of the sources.