As suggested in the stringr package, this can be achieved using either str_match() or str_extract(). 
Adapted from the manual:
library(stringr)
strings <- c(" 219 733 8965", "329-293-8753 ", "banana", 
             "239 923 8115 and 842 566 4692",
             "Work: 579-499-7527", "$1000",
             "Home: 543.355.3679")
phone <- "([2-9][0-9]{2})[- .]([0-9]{3})[- .]([0-9]{4})"
Extracting and combining our groups:
str_extract_all(strings, phone, simplify=T)
#      [,1]           [,2]          
# [1,] "219 733 8965" ""            
# [2,] "329-293-8753" ""            
# [3,] ""             ""            
# [4,] "239 923 8115" "842 566 4692"
# [5,] "579-499-7527" ""            
# [6,] ""             ""            
# [7,] "543.355.3679" ""   
Indicating groups with an output matrix (we're interested in columns 2+):
str_match_all(strings, phone)
# [[1]]
#      [,1]           [,2]  [,3]  [,4]  
# [1,] "219 733 8965" "219" "733" "8965"
# 
# [[2]]
#      [,1]           [,2]  [,3]  [,4]  
# [1,] "329-293-8753" "329" "293" "8753"
# 
# [[3]]
#      [,1] [,2] [,3] [,4]
# 
# [[4]]
#      [,1]           [,2]  [,3]  [,4]  
# [1,] "239 923 8115" "239" "923" "8115"
# [2,] "842 566 4692" "842" "566" "4692"
# 
# [[5]]
#      [,1]           [,2]  [,3]  [,4]  
# [1,] "579-499-7527" "579" "499" "7527"
# 
# [[6]]
#      [,1] [,2] [,3] [,4]
# 
# [[7]]
#      [,1]           [,2]  [,3]  [,4]  
# [1,] "543.355.3679" "543" "355" "3679"