is there a way to count unique dates in R dplyr

We may use match on the sorted unique values of 'Date' after grouping by 'ID'

library(dplyr)
df1 %>% 
   group_by(ID) %>%
   mutate(count = match(Date, sort(unique(Date)))) %>%
   ungroup

-output

# A tibble: 8 × 3
  Date          ID count
  <date>     <int> <int>
1 2000-01-01     1     1
2 2000-01-02     1     2
3 2000-01-03     1     3
4 2000-01-01     2     1
5 2000-01-01     2     1
6 2000-01-01     3     1
7 2000-01-10     3     3
8 2000-01-04     3     2

Or another option is dense_rank

df1 %>% 
  group_by(ID) %>%
  mutate(count = dense_rank(Date)) %>%
  ungroup

data

df1 <- structure(list(Date = structure(c(10957, 10958, 10959, 10957, 
10957, 10957, 10966, 10960), class = "Date"), ID = c(1L, 1L, 
1L, 2L, 2L, 3L, 3L, 3L)), row.names = c(NA, -8L), class = "data.frame")