Players drafted between 1936 and 2014, played TE, in the 1st round, between the 1st and 32nd pick
http://www.pro-football-reference.com/play-index/draft-finder.cgi?request=1&year_min=1936&year_max=2014&type=&round_min=1&round_max=1&slot_min=1&slot_max=32&league_id=&team_id=&pos=TE&college_id=all&conference=any&show=all#drafts::3
1 1960 1 1 Billy Cannon TE RAM 1960 1970 2 2 9 53 133 28 602 2455 17 236 3656 47 LSU
2 1961 1 5 Mike Ditka HOF TE CHI 1961 1972 2 5 8 56 158 78 4 4 0 854 11624 86 Pittsburgh
3 1972 1 5 Riley Odoms TE DEN 1972 1983 2 4 10 54 153 134 25 211 2 396 5755 41 Houston
4 1973 1 6 Charle Young TE PHI 1973 1985 1 3 10 46 187 142 16 80 1 418 5106 27 USC
5 2004 1 6 Kellen Winslow TE CLE 2004 2013 0 1 5 36 105 83 1 7 0 469 5236 25 Miami (FL)
6 2006 1 6 Vernon Davis TE SFO 2006 2013 0 2 8 41 119 117 5 11 0 397 5201 53 Maryland
7 1963 1 7 Pat Richter TE WAS 1963 1970 0 0 8 22 103 1 1 -9 0 99 1315 14 Wisconsin
8 1969 1 7 Ted Kwalick TE SFO 1969 1977 1 3 3 30 108 43 19 175 0 168 2570 23 Penn St.
9 1973 1 7 Paul Seymour TE BUF 1973 1977 0 0 5 11 69 68 62 818 3 Michigan
10 1974 1 7 J.V. Cain TE STL 1974 1977 0 0 2 12 55 37 76 1014 9 Colorado
11 1978 1 7 Ken MacAfee TE SFO 1978 1979 0 0 2 5 29 25 46 471 5 Notre Dame
12 1980 1 7 Junior Miller TE ATL 1980 1984 0 2 3 14 71 45 3 0 0 122 1409 14 Nebraska
13 1963 1 9 Tom Hutchinson TE CLE 1963 1966 0 0 0 5 47 0 19 409 2 Kentucky
14 1972 1 9 Jerome Barkum TE NYJ 1972 1983 0 1 10 44 158 136 3 -3 0 326 4789 40 Jackson St.
15 1995 1 9 Kyle Brady TE NYJ 1995 2007 0 0 13 26 197 175 343 3519 25 Penn St.
16 1996 1 9 Rickey Dudley TE OAK 1996 2004 0 0 5 24 108 87 2 -9 0 221 3024 33 Ohio St.
17 2014 1 10 Eric Ebron TE DET 0 0 0 North Carolina
18 1960 1 11 Monty Stickles TE SFO 1960 1968 0 0 9 30 115 90 222 3199 16 Notre Dame
19 1983 1 12 Tony Hunter TE BUF 1983 1986 0 0 2 11 47 22 4 28 0 134 1501 9 Notre Dame
20 1979 1 13 Kellen Winslow HOF TE SDG 1979 1987 3 5 7 62 109 94 541 6741 45 Missouri
21 1988 1 13 Keith Jackson TE PHI 1988 1996 3 5 7 43 129 105 441 5283 49 Oklahoma
22 1997 1 13 Tony Gonzalez TE KAN 1997 2013 6 14 16 97 270 254 2 14 0 1325 15127 111 California
23 1966 1 14 Milt Morin TE CLE 1966 1975 0 2 8 48 129 64 5 41 0 271 4208 16 Massachusetts
24 1981 1 14 Willie Scott TE KAN 1981 1988 0 0 3 6 98 42 1 1 0 89 766 15 South Carolina
25 1992 1 14 Derek Brown TE NYG 1992 1999 0 0 1 4 105 33 43 401 1 Notre Dame
26 2000 1 14 Bubba Franks TE GNB 2000 2008 0 3 6 18 122 98 262 2347 32 Miami (FL)
27 2002 1 14 Jeremy Shockey TE NYG 2002 2011 1 4 10 48 136 129 1 6 0 547 6143 37 Miami (FL)
28 1985 1 15 Ethan Horton TE KAN 1985 1994 0 1 5 22 116 80 79 241 3 212 2360 17 North Carolina
29 1992 1 15 Johnny Mitchell TE NYJ 1992 1996 0 0 2 16 57 43 159 2103 16 Nebraska
30 1970 1 16 Rich McGeorge TE GNB 1970 1978 0 0 7 24 116 87 1 3 0 175 2370 13 Elon
31 1975 1 16 Russ Francis TE NWE 1975 1988 0 3 11 45 167 148 2 12 0 393 5262 40 Oregon
32 1974 1 18 Reuben Gant TE BUF 1974 1980 0 0 3 16 101 50 1 14 0 127 1850 15 Oklahoma St.
33 1973 1 20 Billy Joe DuPree TE DAL 1973 1983 0 3 8 40 159 102 26 178 1 267 3565 41 Michigan St.
34 1984 1 20 David Lewis TE DET 1984 1987 0 0 1 7 47 32 60 731 8 California
35 1993 1 20 Irv Smith TE NOR 1993 1999 0 0 5 14 95 76 183 1788 15 Notre Dame
36 2009 1 20 Brandon Pettigrew TE DET 2009 2013 0 0 5 20 71 68 284 2828 16 Oklahoma St.
37 1969 1 21 Bob Klein TE RAM 1969 1979 0 0 9 29 145 120 4 14 0 219 2687 23 USC
38 1990 1 21 Eric Green TE PIT 1990 1999 0 2 6 32 120 103 362 4390 36 Liberty
39 2002 1 21 Daniel Graham TE NWE 2002 2012 0 0 7 19 148 117 224 2490 25 Colorado
40 2010 1 21 Jermaine Gresham TE CIN 2010 2013 0 2 4 19 59 52 218 2262 19 Oklahoma
41 2013 1 21 Tyler Eifert TE CIN 2013 2013 0 0 1 4 15 15 39 445 2 Notre Dame
42 1977 1 22 Mike Cobb TE CIN 1977 1981 0 0 1 1 62 19 11 134 0 Michigan St.
43 1997 1 22 David LaFleur TE DAL 1997 2000 0 0 3 7 60 44 85 729 12 LSU
44 1978 1 23 Ozzie Newsome HOF TE CLE 1978 1990 1 3 13 59 198 191 18 135 2 662 7980 47 Alabama
45 1970 1 24 Raymond Chester TE OAK 1970 1981 0 4 10 53 172 131 5 9 0 364 5013 48 Morgan St.
46 2003 1 24 Dallas Clark TE IND 2003 2013 1 1 8 51 143 118 4 40 0 505 5665 53 Iowa
47 1978 1 25 Reese McCall TE BAL 1978 1985 0 0 3 10 117 56 94 1366 12 Auburn
48 1995 1 27 Mark Bruener TE PIT 1995 2008 0 0 10 10 188 139 152 1333 18 Washington
49 2000 1 27 Anthony Becht TE NYJ 2000 2011 0 0 9 12 167 132 188 1537 21 West Virginia
50 1976 1 28 Bennie Cunningham TE PIT 1976 1985 0 0 6 29 118 80 202 2879 20 Clemson
51 2002 1 28 Jerramy Stevens TE SEA 2002 2010 0 0 2 18 121 42 202 2217 22 Washington
52 2006 1 28 Marcedes Lewis TE JAX 2006 2013 0 1 7 29 120 106 297 3583 25 UCLA
53 2005 1 30 Heath Miller TE PIT 2005 2013 0 2 9 40 137 136 1 6 0 466 5273 40 Virginia
54 2008 1 30 Dustin Keller TE NYJ 2008 2013 0 0 3 23 72 49 1 7 0 241 2876 17 Purdue
55 2001 1 31 Todd Heap TE BAL 2001 2012 0 2 8 43 145 131 8 61 0 499 5869 42 Arizona St.
56 2007 1 31 Greg Olsen TE CHI 2007 2013 0 0 5 32 110 84 381 4180 36 Miami (FL)
57 2004 1 32 Ben Watson TE NWE 2004 2013 0 0 8 31 131 95 2 10 0 340 4002 30 Georgia