https://playback.fm/year/1933

No. Song-Artist-Peak Month
 1 STORMY WEATHER (KEEPS RAININ' ALL THE TIME)-ETHEL WATERS-JUNE
 2 SOPHISTICATED LADY-DUKE ELLINGTON & HIS FAMOUS ORCHESTRA-July
 3 GOLD DIGGER'S SONG (WE'RE IN THE MONEY)-DICK POWELL-June
 4 SHADOW WALTZ-BING CROSBY & JIMMIE GRIER'S ORCHESTRA-July
 5 YOU'RE GETTING TO BE A HABIT WITH ME-BING CROSBY-March
 6 LOVER-JACK FULTON,PAUL WHITEMAN & HIS ORCHESTRA-April
 7 DID YOU EVER SEE A DREAM WALKING?-EDDY DUCHIN-December
 8 LOVE IS THE SWEETEST THING-Ray Noble-September	
 9 THE LAST ROUND-UP-George Olsen-October
10 THE LAST ROUND-UP-Guy Lombardo-November
11 Stormy Weather (Keeps Rainin' All the Time)-Leo Reisman & Harold Arlen-May
12 Lazybones-Ted Lewis & his Orchestra-August	
13 Night & Day-Eddy Duchin-January	
14 The Gold Diggers' Song (We're In The Money)-Ted Lewis & His Band-June
15 Yesterdays-Leo Reisman & His Orchestra-December
16 Who's Afraid Of The Big Bad Wolf?-Florence Case,Charles Yontz,Frank Sherry,Don Bestor & His Orchestra-November
17 Hold Me-Eddy Duchin-May
18 Just An Echo In The Valley-Bing Crosby-February
19 The Wedding of Mister Mickey Mouse-BBC Dance Orchestra-July	
20 Alo Alo-Carmen Miranda & Mario Reis-July	
21 Stormy Weather (Keeps Rollin' All The Time)-Guy Lombardo & His Royal Canadians-June
22 The Last Round-Up-Songsmiths,Victor Young & His Orchestra-November
23 Easter Parade-Clifton Webb,Leo Reisman & His Orchestra-December
24 I've Got To Sing A Torch Song-Bing Crosby & Jimmie Grier's Orchestra-August
25 I Like A Guy What Takes His Time-Mae West-April
26 The Last Round-Up-Gene Autry-November
27 Did You Ever See A Dream Walking?-Bing Crosby & Lennie Hayton's Orchestra-December
28 Lover-Guy Lombardo-April	
29 Thanks-Bing Crosby & Jimmie Grier's Orchestra-October
30 April In Paris-Henry King & His Orchestra-January
31 Hold Me-Ted Fio Rito & His Orchestra-June
32 Moon Song (That Wasn't Meant For Me)-Arthur Kassel & His Kassels-In-The-Air-February
33 Stormy Weather (Keeps Rainin' All the Time)-Frances Langford-June	
34 Linda Morena-Mario Reis & Lamartine Babo-July	
35 Lover-Greta Keller-April	
36 Let's All Sing Like The Birdies Sing-Ben Bernie & His Orchestra-February
37 It's The Talk Of The Town-Fletcher Henderson & His Orchestra-December
38 Temptation-Bing Crosby & Lennie Hayton's Orchestra-December
39 The Day You Came Along-Bing Crosby & Jimmie Grier's Orchestra-October
40 Did You Ever See A Dream Walking?-Guy Lombardo & His Royal Canadians-December
41 The Last Round-Up-Bing Crosby & Lennie Hayton's Orchestra-November
42 Shuffle Off To Buffalo-Maurice Cross,Don Bestor & His Orchestra-April
43 The Last Round-Up-Neil Buckley,Don Bestor & His Orchestra-October
44 Shuffle Off To Buffalo-Hal Kemp & His Orchestra-April
45 Young And Healthy-Bing Crosby,Guy Lombardo & His Royal Canadians-April
46 Stormy Weather (Keeps Rollin' All The Time)-Duke Ellington & His Famous Orchestra-July
47 That's My Home-Louis Armstrong-March
48 O Orvalho Vem Caindo-Almirante-July	
49 How Come You Do Me Like You Do-Spike Hughes & his All American Orchestra-July	
50 A Farewell To Arms-Jack Fulton,Paul Whiteman & His Orchestra-March
51 Jazz Me Blues-Joe Venuti & his Blue Six-July	
52 Nao Tem Traducao-Francisco Alves-July	
53 The Moon Song-Wayne King & His Orchestra-February
54 Who's Afraid Of The Big Bad Wolf?-Victor Young & His Orchestra-October
55 I Cover The Waterfront-Eddy Duchin-July
56 Just An Echo In The Valley-Rudy Vallee & His Connecticut Yankees-February
57 Learn To Croon-Bing Crosby & Jimmie Grier's Orchestra-July
58 Hold Me-Hotel Commodore Orchestra-May
59 Isn't It Heavenly?-Eddy Duchin-July
60 We'll Make Hay While The Sun Shines-Bing Crosby & Lennie Hayton's Orchestra-December

*This list was compiled with charts from various 
western industrialized  nations (primarily the USA and UK).